If an adult is no longer able to care for themselves and has no one to care for them, can they be legally forced into a care facility?

It depends entirely on the person's mental function.

If the person is of sound mind and able to understand his situation and the consequences of his choices, then no one can force him either to accept help or to move to a facility. A mentally competent person who chooses to sit at home and rot is entirely free to do so. All you can do is bite your nails until something changes, and keep the offer open.

But such a black-and-white situation is very unusual. More commonly, the person is engaged in a battle of wills about whether other people can be forced to support him at home, or fighting tooth and nail to stay out of a facility, or the combatants are using different definitions of "no longer able to care for himself" and of "force" and "has no one"; and there is room, somewhere, for discussion and negotiation.

Would you like to say more about the person who is resisting care and why and what you were hoping to do about it?

Not enough information in your post to help you.

Would expect this to depend on outcome of court ordered assessment and decision on whether to appoint a guardian. More likely for cognitive failure than just not doing what "you" think they should, but seek advice if you know someone in this situation and are in a position to do so

If the person lives alone and APS evaluates and finds the person can't take care of themselves, then yes they can be forced to go to a LTC. Like said, the court will assign a guardian who will handle looking into the persons finances to see if they can afford their care. If not Medicaid will take over.

Are you referring to your wife?

Given someone with dementia and a danger to self or others a court appointed guardian would be appointed when this person ended up in police or hospitalization situation. Then placement could occur. Why do you ask?

I think that they would be assessed and the state would assign a guardian that would ensure they had proper care.

Depending on the financial situation it is likely that they would be placed in a facility.

If you know someone this applies to, they should get there personal wishes in writing and have a fudiciary lined up to help them receive care when they have no one available. I would contact a certified elder law attorney and find one that is a larger firm with fudiciary on staff, it is safer and you don't have to worry if the fudiciary gets injured or dies, the firm will continue to do what is needed. (www.nelf.org can help you locate an attorney in your area.)