Although not made explicit, the Dying condition strongly implies that the Player-hero must first receive successful first aid to be able to recover Endurance from any source, while there is no such limitation for unconscious characters. Also, the rules consistently link the unconscious status to having 0 Endurance, from which it can easily be inferred that, by RAI, regaining any Endurance brings back the character to consciousness.
However, this is definitely an edge case open to interpretation. I can easily see in the future an errata for the
Flame of Hope Enchanted Reward to prevent unconscious heroes (not just Dying ones) from recovering Endurance. At least, that's what I'm going to suggest to Francesco
It is not our part to master all the tides of the world, but to do what is in us for the succour of those years wherein we are set, uprooting the evil in the fields that we know, so that those who live after may have clean earth to till.