The stakes in these scenarios are life and death. That said, if a player dies in the first five minutes of play, it wouldn’t be much fun for them to simply sit out the rest of the game. GMs might consider having backup characters available, or allowing players to take over NPCs.
Alternately, “dead” may not necessarily mean “gone.” If killed by a zombie or a vampire, a character might come back—albeit with a very different agenda. At that point, that character might become an NPC for the GM to control, or the player might start playing on the GM’s team, attacking their former allies.