But that asides I think Name Lips is on the right track.
Okay, I know there are those other sorts of options... I've used some of them before, and they work to a degree. Right now, that's not what I'm looking for. Right now, this is just a thought exercise to see if we can make this particular house rule work, or if it's a completely worthless idea.
Iron Heroes already uses almost this exact same idea for characters that have fallen to -10 hps or lower. The idea was to first, extend the rule all the way up to 0 hps, and then drop the death penalty to the save DC -10 to include unconsciousness on a failure of -9 or less. (Incidentally, I made a typo to the rule above: The DC should be negative hit point total, not negative hit point total plus ten... I'll fix that.)
Running this past my wife, it has a few ramifications, if you are using this in IH...
The first chance you have of going unconscious is when your negative hit points are equal to your character level + Constitution modifier + 2 (or your Fort save bonus + 2). Once you reach negative hit points equal to your character level + Constitution modifier + 20 (or your Fort save bonus + 20), you can only stay conscious on a roll of a natural 20. Between those two, the chance slowly increases.
The first chance you have of dying is when your negative hit points are equal to your character level + Constitution modifier + 12 (or your Fort save bonus + 12). Once you reach negative hit points equal to your character level + Constitution modifier + 30 (or your Fort save bonus + 30), you can only stay alive on a roll of a natural 20. Between those two, the chance slowly increases.
Plus, stabilizing someone using the Heal action is a standard action... Feasibly, a character who is still conscious, but not yet stabilized could try to stabilize themselves with a DC 15 Heal check (in addition to the 10% chance every round).
So a 5th level IH character with a Constitution of 14 (Fort save of +7) would be disabled from 0 to -8 hit points, would have an increasingly difficult chance of staying conscious from -9 to -27 hit points, and an increasingly difficult chance of staying alive from -19 to -37 hit points. All along, they'd be losing 1 hit point per turn, unless they stabilized.
That character, assuming they never stabilize, could feasibly take up to 4 minutes to die from a mortal wound.
And a 15th level IH character with a Constitution of 14 (Fort save of +17) would be disabled from 0 to -18 hit points, would have an increasingly difficult chance of staying conscious from -19 to -37 hit points, and an increasingly difficult chance of staying alive from -29 to -47 hit points. All along, they'd be losing 1 hit point per turn, unless they stabilized.
The one down side I can see, especially with IH characters, is that higher level characters could become exceptionally difficult to kill... Though near death experiences would be a bit more common, the characters would have lots of time, relatively, to bring themselves back from the brink of death.