I can't afford to take Dad in, but he can't care for himself anymore. Now what?

My father is 67 years old and is recovering from a decade of alcohol abuse that has left him with no assets (and I mean none). He lives with his only surviving sister who is about to be tossed out of the foreclosed on home, and regardless is ready to put him on the street. He makes about $1,400 a month in Social Security, which is just enough money for him to not qualify for most assistance programs (Medicaid) while not enough to pay for really anything. He is angry, depressed, drug seeking, and unwilling to do anything for himself (EX: he demands I find him a place to live but is unwilling to call prospective apartments or go look at places when I come visit - "It's too hard. I'm too tired. I am fine where I am. I'm not going.").

I am in my early twenties and live in a tiny one bedroom with my girlfriend about 2 hours drive away from the sisters house. My GF and I both work and cannot afford to take him in. If his sisters house must be vacated, and she refuses to live with him again (who can blame her?) he will be homeless.

What do I do from here? What facilities will take in someone that requires constant supervision and has absolutely no money? I can't even get him to file any paperwork because he is so difficult.