A set of rules I'm considering for what happens when a PC actually dies.
When you would die, Death comes to claim you. Time freezes, everything but Death and yourself become somehow less than real. You die automatically and are led away, unless you can do one of the following:
Gambling with Death
You can offer to play against Death in a game of skill or chance. You and the other PCs actually play a game against the GM (who represents Death), perhaps liars dice, a hand of poker, a riddle contest. Death gets to choose the game (GMs, pick one you're confident you can win). If you lose, death gets to take one of your companions as well as you. You only get one shot at this each time death comes for you.
You offer Death a substitute soul in your possession, to take instead of yourself. Spells to claim people's souls, such as Magic Jar, are useful here. Alternatively, if somebody has signed a contract saying you own their soul, you can sell that contract to Death in exchange for your own life. The soul should be at least as valuable as your own, but Death might be willing to haggle. Might.
Bargaining with Death
You promise Death something he wants. You might finally kill somebody who’s frustratingly evaded him (such as a lich). You might allow him to possess your body for a time. You might be set a quest of cosmic importance. It’s up to Death to decide if he accepts, and if he feels you’re trying to renege, he can snap his fingers and have you die whenever he wants. If you do this, even though you get to live, your life just got a lot more complicated, and if you die while completing Death's task things will only get worse.
If you insist. Death has 20 HD, passes all saves on a 2+, kills you on a successful hit rather than dealing damage, and is immune to fire, drowning, poison, mind-control, etc. He is a divine being and can, basically, create whichever supernatural effects he wants. You won't win this unless you have an especially clever plan, and even then it will only work once.
If you successfully wriggle out of dying, Death leaves, and you snap back to reality on 1 HP.
Where Does Death Lead You?
The GM makes a judgement call as to where your soul goes after death, based on the virtue of your deeds, any pacts made with supernatural beings, and so on. This will affect your next PC.
If you go somewhere good, treat all 1s when rolling for attributes as 6s.
If you go somewhere bad, treat all 6s when rolling for attributes as 1s.
If your soul is claimed by a supernatural being, as well as this then your new PC is tainted by that being and may have an appropriate weakness (such as double damage from Holy things) and a tell such as an extra finger or birthmark.
If your soul is totally destroyed, you roll up your stats normally. However, your next PC is soulless, and dies automatically when they hit 0HP: no saves, no injury tables, no bargaining with death. Find a way to gain a soul before this happens in order to avoid this.