If you're trying to make dying more of a threatl, I don't think negative HP is the best way of handling that. Maybe just houserule it so that when you hit 0, on your next turn you have one chance to stabilize or you die, with the check being a con save DC 10 instead of a straight d20. If you succeed or are revived by any other means, mark off one of your stabilization boxes. Each additional attempt increases the DC by 5 per previous stabilizations made, so if you go down twice then your second DC would be 15, and if you've gone down 3 times, it's DC 20. Failure is death, and a 4th time dropped is death regardless.
You could balance things out a bit by dictating how easy it is to clear your stabilization marks, but I'd say they go away at the same rate as exhaustion, and any effect that clears one also clears the other (long rest, greater restoration, etc).
The reason I'd go with something like that over simply making negative HP is because negative HP really was only a solution to problems most common at low levels. This idea offers something that can continue for the length of a campaign.
You could balance things out a bit by dictating how easy it is to clear your stabilization marks, but I'd say they go away at the same rate as exhaustion, and any effect that clears one also clears the other (long rest, greater restoration, etc).
The reason I'd go with something like that over simply making negative HP is because negative HP really was only a solution to problems most common at low levels. This idea offers something that can continue for the length of a campaign.