Is POA responsible for checks written to "cash" for the last 5 years?

My mother is POA for my grandmother who is now in a nursing home.

Nursing home told Mom that she is responsible for every check written to "cash" and owes about $10,000 -out of her pocket and can garnish her wages to get this $ if she doesnt pay it- because there were checks written to "cash" in the last 5 years from their joint account and i guess medicare or medicaid - cant remember right now i think its medicare is not going to cover it.

Who can help mom at this point - from being on this site i gather we need to look for something like an "eldercare lawyer" but isnt that going to cost mom money?

So back to the question. IS my mother, who is durable POA going to have to pay this $10,000 and where is she supposed to get the money can they garnish her wages.

Why is it guilty until proven innocent?

Thanks for any advice. We live in New Jersey.