I've been having this odd idea lately.
Namely, instead of using "HP" to abstract out injury, use it to abstract the party's morale.
There would also be a rule, called "bowing out", that allowed someone to absorb damage done, in return for temporarily being removed from the game.
So, for example, the party has 10 HP; the party trapfinder runs into a nasty trap that deals 3 damage; now, he could choose to take the damage, negatively impacting the party's morale (he managed to dodge to the side, but lost his pack with some precious pieces of equipment they needed.) or he could bow out (he gets hit in full by the trap; his leg is smashed, but he insists everyone else goes ahead. After all, they'll need the gold to help fix him up, right? Perhaps there could be rule that lets you bow out with a party mate, giving a "class"-specific bonus; a healer could bow out in this example, letting their party mate recover faster.)
Then, there could be certain "class" features that play with the concept of HP as morale; for example, a leader class could have +2 max HP (their great resolve keeps the party going), and a feature that, essentially, gives the party DR 1/- for the rest of a battle where they bow out (they get downed? The party, in a vengeful mood, go at it with a new ferocity.)
There could be more nuances (I can see an "evil lord" class with the ability to make their minions bow out, or maybe a weapon that deals 1 damage even if the target bows out), such as separating "adventure" HP and "combat" HP (adventure HP being how much you want to keep going with this adventure as a whole, combat HP being how much you are willing to keep going in this battle), but really, this is the basic idea.