I don't know where this feat should be implemented, if at all. I just thought it was a cool idea that would be fun to see added somewhere. It could easily be used as a game-balancing mechanism or a nice enhancement.
Feat/Enhancement Idea:
{Insert Name}: The next time damage would lower your health below one, it is instead reduced to one. This ability has X charges and regains one charge every Y seconds.
It won't make the players immortal like a 100% uncapped dodge buff, because rapid hits could burn through all charges in less than a second. However, it will give some breathing room wherein a single hit means death.
It isn't the worst idea for balancing melee vs ranged, but it's also not the idea I would go with.
It's not important. I just thought it sounded cool.