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While raging, if the barbarian is reduced below 0 hit points, 1 hit point of lethal damage per barbarian level is converted to nonlethal damage. If the barbarian is at negative hit points due to lethal damage, she immediately stabilizes.
If I read it correctly that the ability don't say that you convert damage from the attack that has brought you under 0 hp. It say that you convert lethal damage to non lethal.
As written you get to convert 1 hp level of the total damage you have taken so far to non lethal damage even if you are level 20, the attack as delivered 2 points of lethal damage and you have been brought at a grand total of -1 hp.
I am reading it correctly?
As a added question, how would it interact with Invulnerable barbarian?
If my reading of the power is exact I think it will not interact in any way, as you aren't changing the incoming damage but you are changing the damage you have already received.
I agree with you; sorry about the confusion from the other thread.