What happens if the hospital can’t find a NH to discharge my mom to?

"I am caring for my mother Ann, who is 92 years old, living in a nursing home with alzheimer's / dementia."

Now ur saying she is 85? What happen to the NH she was in prior to the Hospital stay? Guess you should have taken that place 45 min away and then look for another one. Previous posts said she is on Medicaid. If so, transportation would be paid by Medicaid. No, the NH is not responsible for the cost. Nor is it hard to set up transportation. She goes the same days 3x a week so thats what they set up.

The cost of cable and phone can come out of her Personal Needs acct. A small % come out of her SS to be put in this acct for her personal needs. Family is not expected to pay. My Mom never paid for cable in her NH.

Is this patient competent?
Who is the health care advocate or POA for this patient if this patient is not competent to make her own decisions?
The hospital cannot take guardianship. They would give guardianship to the state. The State cannot take guardianship away from the current POA unless the current POA is acting inappropriately. And they certainly cannot take guardianship from a senior in order to put that person into hospice without the patient and/or family permission and they certainly cannot withdraw dialysis in order to KILL a person. The POA or next of kin needs to speak with the Social Services. The hospital may move the patient to skilled nursing unit as the patient no longer needs acute care and they cannot keep a patient who is not in need of acute care while others wait for care. You should see an elder law attorney at once with your suspicions about what is happening if you are the POA or the POA for health care. AT ONCE! Speak first to a Social Worker and tell them that if anyone withdraws dialysis from this patient it is tantamount to signing an execution warrant. This cannot be done without discussion with A) the patient who is first in line to make this decision if mentally competent and/or B) family if patient is not competent.
Meanwhile it is time for the POA for health care to consider what this patient wanted for end of life care, what heroic measures and how long the patient wants to go through dialysis and other heroic measure to maintain life.

That's a long time to be waiting at the hospital but not crazy unusual. Covid is really screwing up virtually everything.

Pardon my ignorance but what does dialysis have to do with transportation?

Eventually, they will find a place. Are you putting any restrictions about where you want her to be placed? Maybe let them put her further away than you might like and try to get her moved later?

How bad is her condition? I think your profile says she's 92. What is her quality of life? Does she want to live as long as possible or is she kind of done? 92 is not a spring chicken (my MIL is 95) and hospice might be something to consider, depending on your answers.

I think the hospital would only pursue guardianship if no one was helping to manage her care.

No, the hospital can't put her on hospice by themselves. Furthermore, if there's no place for safe discharge, then they have to keep her as they currently are.