Self defense is a legal defense. That means the person claiming that they were acting in self defense is going to be doing that, at trial, in front of a jury. That means they have been charged with murder and the jury has to decide whether the defendant was acting reasonably when they killed them. What that means specifically, depends on jurisdiction.
They could also be guilty of a lesser crime than first degree murder. There are knowing, reckless, and acting under extreme duress versions of homicide in most places. All of which still carry jail time.
Having argued self defense in front of a jury, I think it should always be an option for them so long as it makes some kind of sense for the facts.