Can a child get a power of attorney if a person already has severe dementia or Alzheimer's disease?

"but none of us are able to pay for this as she gets Medicare"

Medicare has nothing to do with Long term care. If in rehab, Medicare will pay for 100day days if needed, its not a given. 20 of those days are 100%, the 80 days are 50%. No guarantee that her secondary insurance will pay the 50% or even part of it.

Your problem is the husband. IMO he is responsible for her care. The assets they have together may be 50% hers. If she is entitled to the 50% this goes to her care, gets spent down and then Medicaid gets applied for.

I think you need an Elder law well versed in Medicaid and maybe divorse. I really don't see where you cannot pay for her care. NHs don't care who is paying for the care just thats its being paid. Medicare is a health insurance that will pay for rehab. Medicaid pays for LTC if the person fits the criteria.

No you cannot at this point legally get a POA for her. You can however apply for guardianship with the courts, but that does cost thousands of dollars.
Do you know if her loser of a husband is her POA? If he is, he could at least give permission to place her.
But right now you need to get with the social worker at the facility where your mom is now, and see what your options are. They can help you apply for Medicaid for your mom if that is necessary, as none of you children should have to pay one penny out of your pockets for her care. She is still technically her loser husbands responsibility, and if needed he may have to step up and pay at least some.
You may have to get a elder attorney involved to protect your mom and any assets she may have.
I wish you all the very best.

Is Mom still in emergency respite? If so, the respite facility currently has Duty of Care for your Mom.

Does this facility have a Social Worker? If so, push for a meeting.

A good one can advice what is currently legal & what can be done.

(Or *warning* may try to push you to collect Mom & deal with on your own - forum posters tell of this happening).

A Social Worker can ask for a referral to Geriatrician or Geriatric Psychologist to assess Mom's capacity to decide her living situation. I have seen someone classified as having capacity to decide 1. who would act for them if they couldn't (son in that case) & 2. give their permission to be moved to Rehab - despite signs of dementia/hospital delerium (short term memory being full of holes, no idea on time, date, where currently was).

I’m assuming you want your mother to give you a power of attorney. If she is no longer able to make rational decisions, the legal answer is ‘no’. Anyone who wanted to query the validity could get it set aside. However there is also a practical answer which might be worth considering. If there is no-one likely to question the validity on the grounds that mother doesn’t have legal capacity, then the POA will probably be accepted by agencies like a bank, who have no reason to doubt it.

If someone does want to query it, they will have to show that she no longer had capacity. They will need to take evidence to court in order to prove it. This is not cheap or easy, and courts usually seem loath to say that an elder wasn’t capable of making decisions about their own life, particularly if the decision is obviously a good idea.

So if I were in your shoes, I would think carefully about who might query this, why they might want to, and how they would show that it wasn’t in mother’s interests. I would explain it clearly and simply to mother (eg something specific and relevant that mother understands, not the full legal ramifications). Have a witness there to see that she seemed to know what she was doing in this case, even if she is not fully competent in general.

Of course, none of this helps with the finances problem.