Maybe what is happening there can be connected to looting in wartime. After all, one of the signs of lack of government authority is when people loot in full view of everyone and nobody enforces the law.

A. Regarding “something swept away by the sea” when human choice is involved (at least when they need to choose to do wrong, and not merely choose between two possibilities), is the doubt basically whether to maintain a halakhic categorical imperative?
Maybe it is similar to the novel point of the Mishneh LaMelekh (following Tosafot) that if there is a Jew willing to teach Torah to a non-Jew unlawfully, this is not considered “one side of the river.” And perhaps specifically when there are only a few people, they still need to make a forbidden choice (as in the case of the Mishneh LaMelekh), but when there are many people, the combined weight almost certainly determines the outcome, so individual choice no longer matters much (were it not for the imperative).

B. Why does the fact that the police will try to catch them mean that the objects are not ownerless? The object is going to be stolen anyway, and indeed the person taking it merely accepts the risk and the payment obligation.

A. Indeed, that is one side of my doubt. The number of people makes it almost certain.
B. The fact that the police will try to catch them is only a sign, not a reason. What I mean is that when the store is breached and the object is about to be stolen, that is no worse than a situation where the object is already in the thief’s possession. But after all, it is also forbidden to steal from the thief, because the object belongs to the owner (even though it is not in his possession). So why, when the object is not yet with him, but it is clear that it will get to some thief, should the situation be any more permitted? As I said, that does not make sense. The police are only an indication that the object is still considered to belong to its original owner.
By the way, even if the object is actually stolen, that does not mean the thief will only pay money for it. If the object is still intact, he will return the object itself.

What about the precise definition? Are we talking about theft or robbery? For theft, there is no burglary here. For robbery, there is no force here.

Why is there no force here? Of course there is. Theft does not have to be burglary. A burglar is one kind of thief.

In Maimonides:

“Who is a thief? One who takes another person’s property in secret, without the owners knowing—for example, one who stretches out his hand into his fellow’s pocket and takes his money while the owner does not see. And similarly in any such case. But if he took openly and publicly with a strong hand, this is not a thief but a robber. Therefore an armed bandit who steals is not a robber but a thief, even though the owners know at the time he steals.”

“Who is a robber? One who takes a person’s property by force—for example, one who snatches movable property from his hand, or who enters another’s premises without the owner’s consent and takes vessels from there; or who seizes his slave or animal and makes use of them; or who goes down into his field and eats its produce. Anything similar is robbery. As it says: ‘And he robbed the spear from the Egyptian’s hand.’”

B. I see (Hoshen Mishpat 356) that the reason it is forbidden to buy from a thief is: “for he thereby strengthens the hands of transgressors and causes him to commit other thefts, for if he finds no buyer, he does not steal.” That implies this is not ordinary theft forbidden because the item belongs to the owner. If so, would stealing something that is about to be stolen be permitted?
But perhaps that consideration (“it is not the mouse that is the thief, but the hole”) is itself a categorical imperative. Presumably the thief will find someone to sell to even without me, but still each individual is forbidden to buy, and everyone together tries to block up the hole. If so, the same would apply here: it is forbidden to steal.

Decisor,
This is not burglary. A thief is someone who takes when the owner does not see. A robber is one who takes by force. In any case, none of this makes a practical difference. Taking someone’s property in any form is robbery.

Yehoshua,
You are talking about the prohibition on buying from a thief. I am talking about the prohibition on stealing from him. One who steals from a thief is exempt from the double payment, but still violates a prohibition.
Stealing something that is about to be stolen is certainly forbidden. Either you are a thief, or you are stealing from the thief.
The categorical imperative certainly applies here.

I understand the relevance of a categorical imperative here (and perhaps if “strengthening the hands of transgressors” is a categorical imperative, then it is completely similar to looting from a store, and it would not count as “something swept away by the sea” regarding the prohibition of theft). What I still do not understand is whether there is something here beyond the categorical imperative—meaning an ordinary formal prohibition of theft.
And regarding the ordinary prohibition, I thought that from the standpoint of taking it away from the owner (it is his, but not in his possession), there is no difference between buying from a thief and stealing or robbing from a thief. And in stealing from a thief there is no “strengthening the hands of transgressors,” so it follows that stealing from a thief is forbidden because you are stealing from the thief, not because you are stealing from the owner.
Therefore, stealing from something that is about to be stolen would be permitted (were it not for the imperative):
Not stealing from the owner—just like taking from a thief, “about to be stolen” means it is not in his possession.
Not stealing from the thief—because it has not yet been stolen.
Not strengthening the hands of transgressors—on the contrary, perhaps it weakens their hands.

My questions (last time, with thanks):
A. Is there also an ordinary prohibition here besides the categorical imperative?
B. Can one show from the prohibition on buying from a thief that there is a categorical imperative even in a place where the number of people (who could fail and buy from the thief) makes the outcome almost certain?

There is a prohibition on stealing from a thief, but it seems to me straightforwardly that this theft is considered theft from the owner. See Maimonides, Laws of Theft 1:17.
Needless to say, this does not weaken the hands of transgressors, because the transgressor here is that very person himself. According to your approach, none of the looters is committing any transgression, because together they exempt themselves. That is obviously unreasonable.
As for the prohibition on buying, that is a special rabbinic enactment, so I am doubtful whether one can derive from it a general principle.

Simply speaking, stealing an object from its owner is only when it is under his control.
Stealing from a thief means it is under the thief’s control (through the legal acquisition rules of robbery).
In our case it is ownerless because of “something swept away by the sea,” since the robbery is being done by non-Jews. The categorical imperative would seemingly apply only if they were all Jews and each one had to refrain from the robbery.

Tam, regarding your “simply speaking,” I saw in Hoshen Mishpat 34, in the Ketzot (subsection 3), as you say, that there is no “thief after thief” (and if he consumed it, he is a damager—to the owner—and is not disqualified from testimony). But in the Netivot (subsection 5), it is as the Rabbi says here, that there is theft against the owner’s “ownership” itself. In any case, according to everyone it is forbidden to use the object (at least in a way that harms its value).
As for a categorical imperative that includes non-Jews, a Noahide is also forbidden to rob, and straightforwardly this is the same prohibition of robbery as that of a Jew.

Yehoshua, here I wanted to argue that he is not even a damager, besides not being a thief.
As for the imperative:
Non-Jews are obligated in the seven Noahide commandments. That applies only to the core prohibition, not to accompanying prohibitions. And therefore, in a case like ours of “something swept away by the sea,” straightforwardly they have no prohibition, and the object is literally like something swept away by the sea.
I doubt that the insurance companies and the police will try to get to the looters. More likely they will look for the rioters who smashed and broke into the stores, so even from the authorities’ perspective the contents of the stores are effectively ownerless.

So you agree that in a regular case of stealing from a thief he is a thief, or at least a damager when he causes damage, but you argue that here he is not a thief and not even a damager when he causes damage, because here it is even more “out of the owner’s possession” than when the object has already been stolen? Look at the first response the Rabbi gave me above, section B. Or is this here theft after despair?
I would say that if so, then there are also no accompanying leniencies, and it would not be permitted for them at all in the case of “something swept away by the sea.” It is enough for an accompanying leniency to come together with its limitations. (And the proposed limitation is that only in the case of “something swept away by the sea” is it permitted, because deciding not to take it is not a generally effective decision. But in a breached store it is forbidden to take, because deciding not to take it is a generally effective decision.)
As for the insurance companies and the police, it was explained above that the police are a sign (apparently a sign of the public conception of ownership, and then civil law theory), and therefore even if the authorities do not have the resources or sufficient motivation to catch the looters themselves, the sign still helps.

Here it is definitely not under anyone’s control, unlike stealing from a thief.
As for the accompanying leniencies, they depend on the accepted worldview, and it seems that in anarchy there are no laws anyway.
The police and the insurance companies are a sign that the matter is not under anyone’s control.

Peace to Rabbi Michi.
With all due respect to his Torah learning, I would like to question the attempt to compare this matter to the dispute between Tosafot and the Rosh about whether there is a difference between throwing a stone and throwing a vessel. There, the issue is not despair at all. Rather, it concerns the intrinsic value of the object itself, as in the discussion in the Talmud about whether we go by its initial status or by the moment the vessel breaks. In other words, the question there is whether the object is still defined as having value in such situations.
By contrast, in our case the object will certainly still have value after the person steals it, just as before he stole it. And when we discuss despair, the question is only whether a person has despaired of the object or not. So there seems to be no room to compare it to a discussion about the value of the object itself.
Isn’t that so?

It seems to me that the comparison to that Talmudic passage is in a case where he shot an arrow and someone else took the object for himself, where everyone would agree that he must return it to its owner under the law of returning a lost object, even if we say that the object already lost its value from the moment the arrow was shot. And similarly in the case where he threw the vessel off the roof and someone else saved it—even if it is considered a broken vessel, the object still belongs to its owner.

Avraham Aharon,
That distinction is what first comes to mind, but in my opinion it is not really a distinction. In “something swept away by the sea,” the object does not necessarily lose its value. It may eventually reach the port of Padua in Italy and someone will take it and use it. The basis of despair there (not everyone agrees that it is a case of despair; it may be normative-halakhic-legal despair rather than factual despair) is that the object lost its value for the owner. The same applies here. Now you have to ask: at what moment did it lose its value for the owner? At the moment someone took it, or at the moment the store was breached? And here there is room for the distinction of Tosafot: as long as the object is in place and there is only an external threat over it, it is not considered to have lost its value. Note that this is why I wrote that perhaps one could make it depend on the dispute among the medieval authorities (Rishonim). It is clear to me that it is not exactly the same thing, but in my opinion there is definitely room for it.

In the case of a “broken vessel,” if the second person took the object for himself, would the first one be liable as a damager and the second one acquire it as ownerless property?

Indeed, exactly like “something swept away by the sea.” After all, according to the view that we go by the initial status, and that a broken vessel is already considered broken, if another came and caught it on a sword blade (in the case of the child) or broke it (in the case of the vessel), he is exempt. What difference is there between breaking it and taking it?

How do you explain that one who kills a mortally wounded person is exempt, but if he robs him and sells him, or entices him to idolatry, he is apparently liable?

First, how do you know that in all those cases he is liable?
Second, there is an intermediate state in which a lethal act has been done to him, but he himself is not yet dead. That is enough to exempt the killer, but he himself is still considered alive. (I think he is still obligated in commandments until he dies, and there is no need to get to your examples.) By the way, I seem to recall that they wrote something similar regarding a broken vessel as well.

I did not understand what you meant by “they wrote something similar regarding a broken vessel as well.” In the case of a mortally wounded person, the killer is exempt but the robber is liable (I have no source, but that is what one would assume). But in the case of a broken vessel, from the answer above the damager is exempt and the robber is also exempt (from transgression and from returning it)?

That is exactly what I wrote.
As for the broken vessel, I seem to recall that they wrote that an act of breaking has been done to it, but the vessel is not yet considered actually broken (for example, can it still contract ritual impurity?).