I don’t have a specific situation; I can make one up… The question really is in general, as a matter of principle. Just as, in principle, it is permitted to desecrate the Sabbath to save a life, even though you have to get into the details of each case, is there room to say the same principle regarding theft?

That depends on the question of whether a person may save himself using another person’s money, about which the halakhic decisors disagree (see Bava Kamma 60b, Rashi and Tosafot there, and the decisors). But of course it also depends on many other parameters: how much the captive is suffering, what the consequences are, whether it is possible to pay back the person from whom you stole, whether there are others who are also supposed to participate (why are you stealing from so-and-so and not from someone else?).

So in principle it’s possible; there are situations in which it is permitted from the outset to steal in order to do something, and afterward maybe you have to return it..
Aside from “saving oneself using another person’s money,” does the Rabbi know of situations in which you would say it is permitted?

There is no “aside from.” That is the term for such situations.