Sacrifice (D&D 5e) - are you WILLING to DIE?

Here is an idea I mentioned a few times, in improved form, and in one single post.

In short, it is this: if you want to fight to death, you can fight past 0 HP, but it is dangerous.

The table below is inspired by a similar one in Dark Fantasy Basic.

Here is how it goes: 

When you drop to 0 Hit Points (and are not killed outright, as per the usual rules), you do not necessarily fall unconscious.

Instead, you can choose to fight on if you're willing to fight to the death.

In theory, the player should consider his characters motivations, bonds, etc., but in practice its his choice (with some justification required).

If he choose to fall unconscious, that's all that happens for now.

If he choose to fight on, he immediately makes a death saving throw.

Death Saving Throws
Whenever you start Your Turn with 0 Hit Points, you must make a Special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life. Unlike other Saving Throws, this one isn’t tied to any ability score. You are in the hands of fate now, aided only by Spells and features that improve your chances of succeeding on a saving throw.

Roll a d20: If the roll is 10 or higher, you succeed. Otherwise, you fail. A success or failure has no effect by itself. On your third success, you become stable (see below). On your third failure, you die. The successes and failures don’t need to be consecutive; keep track of both until you collect three of a kind. The number of both is reset to zero when you regain any Hit Points or become stable.

Rolling 1 or 20: When you make a death saving throw and roll a 1 on The D20, roll on the table below. If you roll a 20 on The D20, you regain 1 hit point.

Death's door table:
1 - This counts as two failed death saving throws, instead of one.
2 - Gain one level of exhaustion.
3 - Permanent scar.
4 - Temporary disability.
5 - Permanent disability.
6 - Falls unconscious.
7, 8, 9... - etc... Immediate death should probably be on the table.

You get the idea.

Optional additions:

* While you have 0 HP, once per turn you can ignore one source of damage (up to 10% of your maximum HP), unless it is a critical hit (see this post). [another alternative would be getting temporary HP due to Adrenalin...]

* You do not recover from death saving throw failures until you take a short or long rest. This is meant to avoid abuse such as allowing the paladin to recover a single HP every turn to avoid death.

What's the point?

Letting PCs choose if they remain fighting after mortally wounded is dramatically appropriated... and just plain cool. Sacrifice suits dark fantasy even better than random death, IMO, and it is obviously more suited to epic fantasy too.

Notice they can still die if they choose unconsciousness, but it is a bit less likely. Unless the adversaries go out of their way to kill a fallen character, he might survive anything but a few bad die rolls or a total party kill. An unconscious characters can also be ransomed, etc.

It is cool for the players, too. They get to choose when to put their characters lives on the line. In practice, I've seem players get a bit more mindful of their battles, taking responsibility in their own hands.