My grandfather died about 12 years ago now. My grandma quickly went south mentally. She started spending all of her money and a settlement she got from my grandfather's death on pointless crap. Her house looked like a true episode of hoarders. To stop her, my dad had to take on responsibility for her since his brother washed his hands of her and refused to help. My dad became her caretaker after moving her into his home on the other end of the state. She was awful. He got two hernia's while taking care of her before he couldn't put up with it anymore and had to put her into a home. She also began to deteriorate mentally and physically. She's now at the point where she does not recognize him at all and can't even speak. She just mumbles and moans but she's still alive. Her quality of life is crap but irregardless, she's still living and my dad has had to pay for her care. The money she receives is not enough to cover it and my dad has had to cover the remainder. My dad has been retired since before he brought her to live with him and he is now almost broke. He is being forced to sell his house and hopes to pocket some of the extra money to move somewhere much cheaper. But this has got to stop. He has slowly lost so much over the years for this woman who is forcing him to become destitute. Why is my dad responsible for her? Is there anyway he can just not take care of her considering he's being forced to sell his own home because of her? I don't want to see my dad lose his home of the last 15 years because he decided to take responsibility for her.
But life isn't simple, is it. Because reading the rest of your post, the answer is yes, he can - but no, you know he won't.
But your father does not have to pay for your grandmother's care, particularly not since he cannot afford to and is placing his own financial security at risk. It sounds as though this is a self-sacrificing choice he made long, long ago, and without taking professional advice.
So get him some professional advice. A good place to start is with the staff of the home where your grandmother is a resident. They may or may not offer funding advice themselves, but even if they don't they will certainly know where you can find it. Start asking around.
What kind of home is GM in? Do they have a social worker? If so, Dad should go in and explain he is out of money and ask how to apply for Medicaid.
Another source of help and information would be the Area Agency on Aging.