Let's say, team starts with "n" life tokens.
Whenever an investigator is reduced to 0 health, his miniature is put on it's side, and 1 life token is discarded. As a result of uncounsciosness, he takes 1 Horror and shuffles all his items, dropping one of them in his space at random.
And there is where ways splits:
1)Other investigators must spend an action point to help uncouscious investigator get up. He regains half of his health. At the end of every keeper phase 1 life token is discard for each uncouscious investigator.
2)At the end of every keeper phase each uncouscious investigator gets up with something like 1/3 of his health automatically. This way obviously requires to have less initial life tokens than previous.
If investigators ran out of life tokens and have someone reduced to 0 health - this person dies and eliminated from the game.
For the objectives which require players to be killed, immediately after objective has been revealed, convert all remaining life tokens to health in something like 2:1 or 1.5:1 or even 1:1 health-to-life token proportion. Investigators decide who regaims how much health from this pool.