Death and Injury

When a player character would be reduced to 0 Hit Points, they are put into mortal danger. The character risks dying, with the chances of death increasing depending on how many times the character has dropped to 0 Hit Points over their career.
When a character drops to 0 Hit Points, the player must first check how many Death Saves are marked as failed on that character's sheet. The amount that are marked as such is used to determine whether a Death Die needs to be rolled, and what the number rolled on the die means for the character.

If the character has not dropped to 0 Hit Points before, and thus has no Death Saves marked as failed, then the player must make one save as failed. The character is then set to 1 Hit Point.

If the character does have one or more Death Saves marked as failed, then they must roll the Death Die—a d6 which will determine the character's fate. If the character succeeds on the roll of the die, they are set back to 1 Hit Point.

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When rolling the Death Die, the outcome is dependent on the number rolled and the amount of failed Death Saves, along with a decision by the player. When rolling the die, a success occurs when the roll exceeds the amount of failed Death Saves. For example, if a character has a failed Death Save, the player must roll a 2 to succeed. If the number rolled equals or is lower than the amount of failed Death Saves, then the roll is counted as a failure.
If the Death Die roll is successful, then the character remains alive at 1 Hit Point, gaining a level of Exhaustion. The player must also mark another Death Save as failed, unless they have already failed three, in which case no additional failed saves are to be marked.
If the Death Die roll is a failure, the character is mortally injured, or dies outright. If mortally injured, the character cannot be saved by any means, including magical healing. The character, if mortally wounded, perishes within a day.

Sacrifical Advantage

When a player is forced to roll a Death Die, they may, prior to the roll, ask for Sacrifical Advantage. In this instance, the player would roll a d6 in the place of the standard d4 used. If the player chooses to do so, however, their character gains an injury on a success, and still dies on a failure.
The type of injury depends on the damage type of the attack. Injuries can be permanent, but should ideally have some kind of restoration of functionality through magic or prosthetics.

Concepts
Death saves are now made with a d6

• The "DC" for the save changes based on the amount that have been made
• The "Death Saves" on the 5e sheet track the DC
• The player has to exceed the number, rather than meeting it like with normal dice rolls

The DC scales with every save made, starting at 0, and ending at 3

• All characters start with none of their death saves filled in
• The first time a character would drop to 0 HP, they must fill in one of the dots
• Every time after the first, the player must roll the d6, with the character dying if the number rolled does not exceed the amount of filled dots
• The number caps at 3, making the roll a 50/50 chance

The player can choose to guarantee an injury to roll the save twice

• This puts getting lasting injuries into the players' hands, rather than the DM's and dice's
• A player can only do this once per long rest, as otherwise they could just do this every time they'd drop to 0
• This has to be called before the save

Make a proper injury table

• Rather than having specific wounds, the table contains locations of impact
• Try to have the injuries be hindering rather than debilitating—no paralysis, etc
• What exactly happens is based on the damage type and damage amount. Let's say having a threshold of around 12 damage