Random chance of survival sucks. I'm honestly unsure why they didn't go with some kind of save (Con or Fort) instead of a 10% chance. That's pretty much a death sentence for anyone cut off from his friends.
Personally, if someone is bleedinging out and unconscious, I think it's ok that death is quite likely unless helped.
On the topic of the PC-sudden-death-syndrome...
You're going to have that problem with just about any system, unless you make the death threshold equal to max hit points (which would make most PCs practically unkillable except for SoD effects).
The system as in the original post avoids both problems. The chance of dying in any one of the total of 5 saves is generally low unless you're very far negative, but nevertheless the chance of succeeding on all 5 isn't that good. In short; if you use the house rule as posted in the starting post, PC's will usually face trivial saving throws (fail only on 1) vs. easy threats - but even those saves are risky in fives, so they are strongly encouraged to help their allies
quickly.
You avoid sudden death syndrome by having a large hp buffer, but you avoid making PC's practically unkillable by both limiting the buffers size and by making even -1 hp a risky proposition.
In general, there have been a lot of alternative suggestions, some with good ideas. However, some alternatives are too complex. To each his own, but I think it's absolutely essential that a house rule be as simple as possible. You can remember 5 death saves and a fort save DC, but it's entirely different matter if you mix Con-checks, Con modifiers, Con totals, staggered, etc. stuff. Really, you're best off getting rid of staggered; it's totally pointless and doesn't add anything to the game as is since it's so extremely unlikely to matter.
Simplicity really matters,
especially for house rules. I generally aim to make house rules in my games simpler and shorter that the PHB rules they replace.
So, to anyone still reading this thread, I strongly suggest taking a look at the original posted house rule, which can be summarized in one paragraph:
A creature with negative hit points is dying. The moment it drops to negative hit points and again each round later, the creature must make a Fortitude save with a DC of 1/2 of its negative hit points. On success, it loses 2 hp, but on failure it dies. The creature stabilizes automatically on the fifth save after it last received other damage; so a dropped creature must save immediately and then 4 more times if it isn't healed or hurt in the meantime.
No staggering, no new types of roll, no requirement to combine multiple stats - just a fort save. Stabilizing effects such as healing work normally.
If you want to change this, I recommend you make it
even simpler, for instance by removing the 2 damage on a successful save and adding a 6th save instead, say.