If I have power of attorney for someone, can I be held responsible for that person's debts in the event of death?
You should not be held liable for the principal's debts or other financial troubles unless those difficulties result from dishonest or grossly irresponsible acts on your part.
As long as you are scrupulously honest, careful with the principal's money, and faithful to the instructions given to you in the power-of-attorney document, you take on little legal risk when you agree to serve as an agent.
Also, you should know that your job ends when the principal dies. At that point, the executor of the principal's will steps in to wind up his or her affairs. If there are debts to be paid, the executor will pay them out of the deceased person's assets. Of course, if you were jointly responsible for the debts to begin with -- for example, because you are married to the principal and you took on the debts together -- you will have to pay.