Lets assume you receive a very hard hit that drains all your life. The draining might last for 0.5 second -ish before you are dead. First, the stun after taking damage + the time needed to swing/shoot is already too long to get out another attack before dying.
But for the sake of this suggestion lets assume you COULD get out an attack when you are actually a walking dead - why should you be granted this luxury when you have already been defeated ?
This is why:
Ya know that scene in The Fellowship of the Ring? The one where Boromir gets shots like a bazillion time and still kills some uruk before croaking?
That's what we shall see.
But gotta agree with Joker. It's a nice idea, but needs some more thinking. +1 anyway.