Dementia patient owes back taxes, but cannot pay. Any advice?

I would think a payment plan would be the only option: are you talking property or income taxes??

What's the old saying..the two things in life that you can be sure of are Death and Taxes!
Taxes will have to be paid.
Some will accept a payment plan you need to work this out with whatever agency is demanding payment.
The person that is POA or the spouse is responsible for setting things right. If the spouse is not a joint owner that might change things.
This might be best discussed with a lawyer well versed in Elder Law. The other option, the person that does taxes for this person might have some ideas.

Profile says u care for ur husband. If this is correct, don't u file jointly?

If not ur husband, who is the person? Does he have a POA, because this is part of their responsibility.

Back taxes in IRS, State or property?

If these are federal taxes, their POA best contact the IRS because the IRS will garnish wages including social security. They can also levy bank accounts.