Liability of attorney-in-fact My wife has durable power of attorney for her…

Liability of attorney-in-fact
My wife has durable power of attorney for her mother who resides in a rest home and is physically incapacitated. Hse had a prior credit card debt that was turned over to collection- with interest and penalties-$11,000. Mom’s income is from SS and is barely enough to pay her rest home expenses. The collection agency has stated to us that since my wife has power of attorney, that my wife and I are liable for this debt and it could ruin our credit if we don’t pay it. Is this true?