If a dying creature has an amount of negative hit points equal to its Constitution score, it dies.
According to RAW, is this the dying creature's normal Constitution score, or it's adjusted Constitution score?
I.e., if a creature has their CON damaged, does this affect the negative hit point total needed to die?
I would say it works the same as other permanent vs. temporary ability bonuses. Drain affects the hit point total needed, but damage does not. Likewise, a temporary bonus (such as from raging or a spell) would not affect it but a permanent bonus (that has been in place for more than 24 hours) would.
Nothing official, but I think it fits the precedent that strength damage doesn't affect carrying capacity and intelligence damage doesn't affect skill points.
Found another discussion here that seems to cover the question... it's based on your Constitution score, which is only impacted by drain/permanent ability bonuses.
So it seems a character with a normal CON of 12 that takes 8 CON damage would still need to hit -12 hit points to die.
Can anyone confirm?
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There is a difference between Ability Damage (which does not change your ability score, only applies a penalty to the bonus from the score), and Ability Drain (which actually lowers your score).
Using your example.
Example A (Damage/penalty): character with a normal CON of 12 takes 8 con damage, their CON is 12, but they would apply a modifier of -4 to all CON based checks, and they would still need to get to -12 to be dead.
Example B (drain): character with a normal CON of 12 takes 8 CON drain, their CON is now 4 and would be treated as thus for all things that deal with CON, this would mean that they would only need to be dropped to -4 to be dead.
Turns out it was a moot point... the CON damage came from an ability called drowning touch, which the character was immune to because they had drunk a potion of water breating. Still, this is good to know for the future.