A lot would depend upon the nature of the thread and the effect of the bullet. The legitimate purpose of shooting someone in self-defense is to neutralize the threat. If that happens to kill the person, fine, but the purpose is supposed to be to stop the attacker.
In many scenarios, I would not expect that someone who had just shot someone else would be inclined to give first aid, but I would expect in other scenarios (e.g. if one knows that the attacker is generally a good person but has 'snapped' for some reason) one might be forced to use deadly force to stop the attacker, and yet not particularly want the attacker dead. Killing the attacker would be preferable to not stopping the attack, but if the attack can be stopped with the attacker surviving that may be preferable still.
I am having a hard time putting together a situation where I am in fear for my life yet I can’t find another solution except deadly force. If you think you are going to be involved in such a thing I suggest that you get some tear gas or a Taser. I would stay away from using deadly force unless you are prepared to defend yourself before a jury.