I have been experimenting with an 'over-damage' rule myself for players, though not a lot of input - yet. When they are reduced to 0, the over-damage is converted to death saves. For every 10 points of damage past 0 you would've been reduced, you start with one failed death save. Over damage by 30 or more hit points, and you're killed outright (save using one of my in-game resources to save lives). Over damage by 20 or more, and your fate hinges on a single d20 roll unless you're healed. Since I use non-cyclic initiative, it does add a bit of dynamic tension - "the cleric has already gone, will the cleric go before the next death save is needed?" - sort of thing.