Okay, that sounds like a really tough situation for the owners and the dog. It's definitely not a decision to take lightly. Before considering euthanasia, have they consulted with a veterinary behaviorist? Aggression can stem from so many things – pain, fear, anxiety. Perhaps a professional could identify the root cause and create a behavior modification plan. Even a slight positive slope in behavior could mean the dog has a chance. Finding an experienced trainer specializing in aggression might also offer alternatives. Good luck to them.