No. They should be careful if they sign for any services on behalf of the person they are POA for; you sign "John Doe in his capacity as POA for James Doe".
You are not personally responsible and should always be careful of the way you sign so you make it clear you are signing as you were instructed legally. Some places prefer Jane Dow, under Power of Attorney for Alice Adams. And some want you to sign Alice Adams, by Jane Dow, POA in fact. Etc. Just make it clear you are signing FOR HER. If your answer is if you are responsible for paying her debts out of her money, then the answer is yes. You are acting for her. So you are handling her bills just as she would handle them were she able. Do seen an hour of time with an attorney if you are at all confused, so that you don't make mistakes that could come back to bite you.
Why do you ask?
Is it because somebody is demanding money from you and trying to tell you that you are liable?
Or is it because you are being asked to act with POA for someone, and you're concerned that it might mean taking on more than you want to bargain for?