For the source text click/tap here: Chullin 121
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If a Jew slaughters a non-kosher animal, then while it is convulsing, it cannot be eaten by anybody: by a Jew, because it is non-kosher, and by a non-Jew, because slaughter does not make it permitted for him, and he must wait till the animal completely dies. Nevertheless, if a Jew slaughters a non-kosher on behalf of a non-Jew, then, since the Jew's intention is to prepare it as food for the non-Jew, it, too, is susceptible to ritual impurity of foods while it is convulsing. Thus, paradoxically, it cannot be eaten, but it is already considered food. The same would be if a non-Jew slaughters a kosher animal.
We discuss the halachic vs pathologic definitions of death:
Biologically, dying is a continuum; ontologically, halakhah recognizes a real transition from living organism to corpse; juridically, however, different areas of halakhah may locate their operative thresholds at different points in that transition.
Hence the mefarkeset is neither simply alive nor simply dead for every purpose. It is the paradigmatic demonstration that a single biological reality can sustain multiple, non-identical halakhic predicates without reducing those predicates to arbitrary legal fiction.