What you hit you buy. That includes the consequences for killing a person or injuring them.
Yes and/or no. With every shooting, there are both legal and moral implications.
From a legal standpoint, as least in my reading of Georgia's criminal code, if you are involved in a legally justified self-defense shooting and you accidentally injure an innocent person, you are not guilty of a crime if your action was not done in "a willful, wanton, or reckless disregard for the safety of others who might reasonably be expected to be injured thereby." Although Georgia is where I live and the laws differ from other states, my understanding is that the same idea is generally true for every state.
For discussion purposes, here is the verbatim text of O.G.C.A. Sections 16-2-1 and 16-2-2:
16-2-1.
(a) A 'crime' is a violation of a statute of this state in which there is a joint operation of an act or omission to act and intention or criminal negligence.
(b) Criminal negligence is an act or failure to act which demonstrates a willful, wanton, or reckless disregard for the safety of others who might reasonably be expected to be injured thereby.
16-2-2.
A person shall not be found guilty of any crime committed by misfortune or accident where it satisfactorily appears there was no criminal scheme or undertaking, intention, or criminal negligence.
For example, if an armed intruder rushes you, you shoot him, your bullet hits him, and then overpenetrates and hits an innocent bystander, you would not be guilty of a crime because there would be no intention to harm the innocent person or criminal negligence on your part. That's pretty clear given you actually hit the BG.
On the other hand, if you fire a warning shot and that bullet hits a kid in his tree house, a jury could easily find that your action demonstrated a willful, wanton, or reckless disregard for the safety of others who might reasonably be expected to be injured thereby. The same could likely be said if you fired multiple rounds at a fleeing BG who is running through a playground full of kids. You get the idea.
All of the above is based on your not using some oddball type of ammo that you
expected would overpenetrate, although I can't think of any such thing except some freakish bullet you made yourself.
But then there's also the moral element. Even if you are legally justified in your actions, I believe every upstanding citizen who embarks on his or her own self-defense has a moral obligation to select a means of self-defense that minimizes the risks to innocents as much as is practical while still providing a high-level of effective self-defense.
The answer to that moral equation will not always be HP. From my reading of the literature, effective self-defense in .380 ACP is likely best accomplished with FMJ, while .45 ACP is likely best accomplished with HP, and rifle and shotgun ammo choices may require entirely different calculations.
Both the legal and moral elements must be balanced. And as always, no matter what choice someone else makes, YMMV.
P.S.: This does not address any civil liability. However, if your self-defense justification is strong in a criminal case, it should see you through a civil suit.