I don't think they have any liability. What they did was legal. It may have been foolish, but the law allows for it.
I think most of the outrage over this incident is the consequence of people thinking nobody should have the right to attempt to detain a suspected burglar with guns, and especially if he's black.
Had this been a white guy, nobody would give the slightest crap that he got shot trying to get away from people trying to arrest him.
I can't say what laws are in GA, but I find it highly unlikely that it's legal to chase someone with a loaded shotgun just because you caught him trespassing. You are correct in guessing that had be been white, nobody outside of that town would care. I could also guess that the deceased's family would sue and probably win a huge civil suit against the FB and his dad