Allowing Healing at 0 HP?

One thing I am thinking is that players do not instantly die at 0 HP but can survive on the brink of death for a number of rounds equal to their constitution modifier. This helps in many cases as Good Clerics can gain XP by saving a character on the brink. It also gives more suitability and realism as in most editions of D&D there is a negative HP survival. Would this be a viable option?

Dungeon World don't have rounds. I have don't have them roll directly, but allow for the players to tell me the last time [The Character] was badly hurt, or who saved them or who they wished they'd kissed if they took their last breath now. This allows characters to help, if fictionally positioned to do so, or at least react to their friend's last moments, at least emotionally.