I love Death & Dismemberment Tables, but I get tired of looking them up. So how about an easily remembered rule?
When you reach 0 or negative hp:
Subtract 1d10 from a random attribute (1d6).
The player can choose:
1. Pass out from blood loss until you receive enough aid to get back up to positive hit points,
2. Stay on your feet like a bad-ass, but take a Permanent Injury.
If you are injured again, you have to roll for Death & Dismemberment again.
Keep track of negative hit points—you have to recover them before you can heal your positive hp.
Attribute points take a week of full rest per point. Multiple attributes can recover at the same time.
Write down a serious injury, such as a lost limb, next to the affected attribute. This is now a Disadvantage, whenever you use that attribute in a way that would be hindered by the injury.
The Player gets to decide what the Permanent Injury is, although it has to make sense with the attribute affected. Lost limbs work nicely for STR and DEX; torso and viscera problems work for CON; head injuries and memory loss for INT; eyes and ears for WIS; and anything that will make people wince when looking at or listening to you for CHR.
This assumes you are using roll-under attribute checks. And it steals the idea of pairing attributes with descriptors from Whitehack.
You could potentially stay on your feet for a long time after hitting 0 hp, but you’d be choosing long term disadvantage for immediate benefit, which is something you would only do in desperate circumstances—all rising up with gritted teeth, “Ignore the ribs puncturing my lungs... Arm missing... Left eye gone... Mustn’t… give… up!” Which seems like a good choice to present to a player.
Is 1d10 for attribute loss too harsh? Not harsh enough? Calibrate to the level of lethality you prefer. If you use a d6, then pretty much the only way a PC could die would be to choose to keep getting up. If you use a d20, folks will die as often as not.