Since I have POA for mom, I don't want her to be responsible for my unpaid debt. Could this happen?

Agree: your mother's money is not your money. Your creditors have no claim on it. And neither have you, by the way - even if you wanted to, you couldn't use it to pay off your debt.

You shouldn't have your mother's funds in an account with your name on it. In that case, a creditor could attach the account and went know the difference, wouldn't know it was your mother's money. Your mothers account should be your mother's account with you as an authorized signatory, and your signature should always include your name followed by "as POA" or "attorney in fact" (this depending upon your state and what the banking requirements are there).

Being POA is for when your Mom can't physically or mentally handle her own affairs.. As long as you keep Mom's accounts separate than yours then she isn't responsible of your debt..