Maim Rule

Nobody likes a boring character death, even less so when you put weeks worth of thought into your character.
So whenever a character fails three death saves, instead of dying the player can choose to use the Maim Rule. The Maim Rule cannot be claimed when a character suffered a situation of instantaneous death (like falling down a 1000ft cliff) or when a character is in a situation they would immediately take damage and start dying again (like drowning at sea or standing in a wildfire with no ally to help save them).
When using the Maim Rule, instead of death, the character suffers a severe wound represented by one (1) Maim Point. A character can have up to two (2) Maim Points active, if they have reached that number and would suffer a third point, they die instead.
The effect of the severe wound depends on what caused the damage, a physical attack could have severed a limb, or magic damage could have caused loss of mental functions. Choose whichever seems more appropriate. 
The mechanical effect will be disadvantage on two appropriate ability scores and all abilities tied to them. That includes weapon attacks or rolls made to determine a hit/miss of a spell if the ability score tied to it was affected.
To reduce the number of Maim Points you have, you need four weeks of undisturbed rest (downtime), as well as medical care. This care can be either magical or physical, but will consume materials worth 1000gp either way. At the end of this, you remove one Maim point from your character.
If you can't afford either the time or money needed to reduce your Maim Points, you can get accessibility tools to remove the disadvantage from one of your ability scores. For example a severed leg (disadvantage on dexterity) could be replaced by a prosthetic leg, a mask could hide your hideous face, an animal could be trained to act as your guide etc. Get creative!