My recollections from law school:
Felony murder is the doctrine that applies. There are different types and it varies by jurisdiction. For example, in every FM jurisdiction, all accomplices are on the hook for the death of a victim. In most, all accomplices are on the hook for the death of another accomplice. In some, the death must have been reasonably foreseeable (an example of a death that wouldn't be foreseeable would be a white collar felony committed by an accomplice who had peanut butter on his fingers from lunch and a victim dies from a peanut allergy after touching paperwork).
As for castle doctrine, it's important to know that we have common law castle doctrine in Nebraska (and all other states that I'm aware of). Under that, anyone forcibly entering a dwelling with the intent to commit a felony inside may have force, up to and including deadly force, used against them to repel them from the dwelling. The intent to commit a felony inside is almost always implied by the fact a person is forcibly entering the dwelling. The main time it is not is when the person has a legal right to be in the dwelling. There is no "duty" to retreat in the home.
Typically, should a person be charged and taken to court, they admit that they killed the intruder, but must prove the affirmative defense of self defense. If, however, the judge finds that the CD applies because the shooting was in the home and the intruder was forcibly entering the home, the burden shifts back to the prosecution to show, beyond a reasonable doubt, that the shooter did not have a reasonable fear (i.e. the prosecution must prove what the shooter was thinking). That is such an insurmountable burden that I've never read of a case where the prosecution kept going once it was determined that the CD applied.
The statutes in those states on the maps expand this to make the CD apply to your vehicle and/or business, some provide a presumption against a finding of wrongful death for the death of the intruder.
I don't have a lot of time these days, but I might put together an article on CD for Nebraska that could be posted on the site and given to our resident CCW instructors.