Of course hit points are abstract... it's a game, right? And it plays by the rules. One of the rules says that as long as you have > 0 HP you're alive and kickin'.
The attempts to improve on hit points have been legion. Eventually it's up to DM to devise a critical hit system that will take care of all those hacked arms, broken legs and ruptured organs (see Torn Asunder by Bastion Press if you want one on a plate).
A simple rule is to apply the effects of fatigue (-2 to attack, AC and saves) when someone loses half their max HP and exhaustion (-4 to above) when they lose 3/4 their max HP. Any combatant that is not subject to death by massive damage is also not subject to this effect.