I think instead of stabilization during bleedout, it should be permitting people to heal themselves during combat under the stipulation that the healing rate is slowed down by half. It would allow you to at least gain a pip of health back and continue fighting just a bit longer, while maintaining the inability to heal yourself when downed and whatnot. If you're still up and can fight, you can prolly patch yourself up, like jab a morphine syringe or something into yourself, or bandage yourself to staunch bleeding so that you don't pass out from blood loss after the fight ends.