As an estate attorney, I am often asked "am I responsible for my deceased relatives debts?" The answer is almost always "no." Unless you are a joint debtor or co-signor, you are not responsible for your deceased relative’s debts. I have included a link to my article which discusses this issue with more detail.
So long as you have not agreed to be responsible for your parents debts you will not be and being their POA will not change this. When acting as their POA be sure to make it clear on everything you sign that you are acting as their agent and not acting on your own; otherwise the creditor may come after you claiming it was your debt.