IMO, this is where expanding ammunition comes into play. LRN (or other non-expanding) bullets will surely kill someone if they poke a hole through something important, but the person may not realize they're dying. I have read incidents of people shot with relatively low-power non-expanding handgun ammo who didn't even realized that they were shot until later. This is a very bad thing.
Attackers who don't know they have been shot, may be dying, but they don't realize it and that is very bad for a defender. That means that the attacker keeps doing whatever he was doing because there's no particular incentive to stop doing it. Presumably whatever they are doing was pretty horrible from the defender's standpoint or no shots would have been fired.
My theory about expanding self-defense ammunition is that one of the major benefits is a "notification effect". The increased deceleration and larger temporary stretch cavity due to expansion applies more impact force to the attacker and creates a "blunt trauma effect" respectively.
A bullet is a combination of a penetrating wound (like a stab wound) and a blunt trauma effect (like getting hit with an impact weapon). The straight penetration (permanent hole) is the stab effect and the temporary stretch cavity is the blunt trauma effect. The penetration is what is most likely to make the wound lethal, but if there is very little temporary stretch cavity, a distracted (or chemically impaired) attacker may not notice the injury. The blunt trauma effect isn't as likely to be lethal (although it can be devastating to tissue that won't stretch--things like livers and brains) but the attacker is quite likely to notice it.
Rearranging priorities is very important. Some years ago, the results of a large batch of FBI wound channel data was put online and I did some wound channel volume calculations from it. Turns out that a bullet from a typical service pistol caliber destroys 2-3.5 ounces of tissue. As a percentage of a 180lb person, that's about 0.07% to 0.12%. Said another way, a round from a typical service pistol caliber leaves a person 99.88% to 99.93% intact. Breaking a person down to ineffectiveness a tenth of a percent at a time is a daunting task. But if his priorities turn to saving his own life by breaking off the attack and seeking medical help, even if he turns out, in the final analysis, to not be especially badly injured, that's a win.
People are very prone to having their priorities rearranged. The vast majority of "stops" are psychological in nature. But there are still cases when the attacker isn't rational for some reason and that means we don't want to give up too much penetration. We want a balance of penetration and expansion--pretty much just what the FBI requires for their ammunition.
