If a sprite's code is damaged, it faces deletion. But typical sprite "fighting" doesn't damage code, merely changes variables and triggers subroutines - including the "death" subroutine.
Usually when a sprite "dies," it goes into a sort of stealth mode, with many of its variables turned off. It becomes temporarily invisible and intangible to other sprites.
At that point, the game usually retrieves the sprite and stores it until it's next needed. But of course, we're outside of our games now, so that doesn't happen.