does the person given health care power of arr. become responsible for debts of patient
No, she will not--you can assure her of that. An agent or attorney-in-fact (those are the names for the person given power by the power of attorney) has the authority to act for the principal (the person giving her the POA) but does not become liable for any of his debts or obligations. It's similar to how the manager of a restaurant, business, or store can make decisions for the business, sign agreements or invoices for it, etc. but it's still the business, not the manager personally, who is liable. Similary, a health care proxy also does not make the person getting the power liable.