You got your UD in my HD!
Someone's probably done this before, but it seems fun, so I'm writing it down.
Vigor Dice
Player characters have an attribute that represents their physical wellbeing, called Vigor. Vigor is tracked with a step die, which starts at a d8 for fighters and a d6 for everyone else. (You could give magic-users a d4 if you want them to be extra fragile.)
Attacks and hazards deal fixed damage. When a character takes damage, they roll their Vigor die. If they roll above the damage, their Vigor holds steady. If they roll equal to or below the damage, they step down their Vigor die to the next lowest die size. When Vigor steps down below d4, the character is Wounded: they're incapacitated and suffer a serious injury, and they may die. (Or maybe they just die, if you want to be extra spicy with it.)
Okay But Why?
Something I like about hit points is that they do that thing you see in adventure movies where a character gets beat up, knocked around, winded, and bloodied, but doesn't actually slow down much. They show up in the next scene with a bandage and some bruises, maybe they wince a bit, but they keep going. Then, at a dramatic moment, they finally get stabbed or shot or there's a loud crack! and something breaks, and that's when the injury is real.
But sometimes you don't want to be writing and erasing a number over and over again on your character sheet. Maybe you want a little more uncertainty about when that dramatic moment happens.
Also, damage values are fixed because I don't want every hit to be a chain of rolls. And for NPCs, probably just use regular HP or something, track it with tally marks. Something like this is less bookkeeping for an individual PC, but if you have multiple NPCs to track, it'll be a pain.
I've seen lots of versions of just using hit dice as health before. I can't seem to turn up most of them with my googling attempts, but I did remember that DURF has a version of this. The main difference here is that the damage doesn't accumulate: each instance of damage is a separate roll, and there's only one hit die to roll, not a pool. As a result, leveling up is less effective at improving survivability (as, at most, you might increase your Vigor die size), but you could get lucky and just keep on surviving by the skin of your teeth. Plus, you don't have to track accumulating damage over the course of an adventuring day.
Anyway! Could be fun. See you next time with a weirder version of this Vigor die thing that I'm actually testing out.