Answer

The statement of the school of Hezekiah regarding those liable to death penalties who acted unintentionally is an important Talmudic topic, and I have wondered about it more than once. The definition is that if this is an act for which there is a severe punishment, then even if he does not actually receive it, that exempts him from the lighter punishment. That is, this is a rule about the transgression itself (the punishment is only a sign, not the cause), and not about the punishment. That is the definition. Now for the explanation.
To understand this, we also need to ask, even in the regular case, why is someone exempted from punishment under the rule of "he receives the greater penalty" at all? Seemingly, he is liable for both punishments and should receive both. As the saying goes: if someone ate garlic and his breath smells, should he go back and eat more garlic? It seems that the exemption from the lighter punishment comes so that we do not diminish the severity of the more serious transgression. We want to sharpen its severity and not let anything else overshadow it. For example, if you murdered a person and in the process also tore his clothes, we would not execute you and also collect a coin from you, because that makes a mockery of the murder. Someone who murdered—one may not view him as anything other than a murderer. It seems that this is also why a free person has no monetary valuation.
If that is the explanation, then it is certainly understandable that this applies also to those liable to death penalties who acted unintentionally. The severe transgression was still committed, and there is no need for him to be actually punished for it in order to be exempt from the lighter one. We want the only thing before our eyes to be the murder itself.