I'd treat it like fast healing--once a character is dead, the healing ability stops. (whereas regeneration makes it very clear it operates no matter how much damage has been taken unless a special method is used to stop it)
I've been planning on running a Rise of the Runelords game for awhile now. And I just came across The Scribbler's stats and one of them has me asking questions. Mainly due to his Ability Healing Special Ability allowing him to heal from ability damage. Would dropping him to 0 con kill him out right or would it be like regeneration rules knocking him out but not dead until killed by other means?
The Text from the ability
"Ability Healing (Ex)
The Scribbler heals 1 point of ability damage per round in each damaged ability score."
Dropping him to 0 Con still kills him as normal. If he wasn't killed for some reason, he'd continue to heal ability damage as normal. I'm assuming he's got the Divine Guardian template or something similar.