What happens in a case where no power of attorney exists?

I don't even know if I posed that question correctly or the right place but here goes...... To explain further, I was asked to be power of attorney for my father. No one in the family wants to deal with him. I suppose many years of violence and abuse has caught up with him. He is stuck in rehab, beyond repair. Ate up with diabetes because he refuses to take care of himself, broken hip and who knows what else. My question is "in general" what will happen with him if there is no one left? I imagine the state would liquidate his assets and put him in a group home until he passed away but thats my best guess. I know there are many factors in play but I would like to have some idea that he is not totally hopeless. Thank you for your time.