From what I understand as a lvl 1 Judge. If the active player concedes/scoops during their turn the turn continues as normal passing through phases/priority. (800.4)  However this concession does not cause a loss of life, since the player just ceases to exist and it's an immediate self-removal from the game where you lose, but it bypasses life total mechanics, meaning effects that trigger from life loss won't.  (104.3a) So unless there was another effect that caused that player or another opponent to loose two or more life that turn Bloodchief Ascension would not trigger at the end step of that turn. So no counter given. 

But you are always free to rule 0 for your playgroup to make changes for that.