When someone designates another with Power of Attorney, the designate agrees to manage that person’s affairs on his or her behalf.
So long as all business is transacted in that person’s name in a legal manner — the ‘legal manner’ being an important element — the designate cannot be made liable for the debts of that person or his/her estate.
Only the person (or the estate of the person) who created the debts will be responsible for debts incurred; the designate will not be personally responsible for those debts.
See all of the legal documents needed to grant and rescind Power of Attorney.