In Dead Space series we switched to the health bar based system when you can heal, so in most cases you can just heal yourself or even revive. Dead players were then later reused to necromorph team or even secondary characters for end game (e.g in DS3).
You can have all sorts of elimination mechanics, depends how long you want the game to be.
Yea that was also something that was used in many games over at BHP, I think DS4 had the most side quest objectives due to being pure RPG.
That's a good idea how to monitor the quests system too.