If someone's heart stopped in a hospital, then an alien possessed their dead body and said "I was just born, this is my body now, your guy was dead" I don't think anyone would argue that the person's heart could very much be restarted (assuming otherwise healthy) and the alien has no right to use someone else's bits.

A better analogy would probably be, if an alien used the body of a cryogenically frozen person that we KNEW could be revived with 100% certainty.