The PCDs usually disappear when a character disappears. There's been a couple occasions when a character has been able to keep the PCD of another's when they disappear (because they were particularly close to them, had extensive CR, that sort of thing). That's really the only time that they don't vanish.

If they just die, their same PCD would still be there when they come back. Resetting, their old PCD would be gone, and they'd get a new one (so like disappearing, then).