Would I be financially responsible for my aunt's debt if I become her financial POA?

I applaud you for wanting to care for your aunt and protect her. I can remember my MILs granddaughters showing up with their hands out the day her SS check hit her bank account. Never failed.
But do be aware that there will be a learning curve on her families part that the bank is closed. You might also want to pay attention to her valuables in her home.
She may also have a problem with turning them down.

Remember she can always change her mind about who she wants for her POA and if she wants to spend her money or give it away she can, assuming she’s not incompetent.
I would spend a little “what if” time with her to help her remember why she’s doing this and keep her strong. 

Make sure she understands the cost of ALF and NH should her health fail and that be in her future.
Should she need Medicaid her financial records will be audited for gifting for five years going back. You might want to take a look at her past bank statements to see when that five years might be starting. See if there are bills she’s paying for others that are draining her account. See if she has co-signed for loans, automobiles etc.
See if she has a mortgage or worse yet, a RM.
Good luck. Let us know how it goes.

One other caveat - never sign anything with your own name. Sign as follows: "Aunt Mary, by Vicster under POA".

Vicster, first of all, as Countrymouse above had mentioned, you will not be responsible for your Aunt's debts if you become her financial Power of Attorney. You job would be to make sure any bills are paid from her money only [including her husband's retirement].

Set up an appointment with an "Elder Law Attorney" to have the Power of Attorney drawn up. The Attorney may want to see your Aunt's Will, if she has one, to be sure it reflects current State laws. The Attorney might even suggest a Medical Directive which tells the family her wishes for her health care. I know I was sooo glad my Dad had one.

Then after the POA is completed, you and your Aunt go to her bank and have paperwork done to allow you to sign her checks. The Bank Manager will walk you through this. Then have all new checks and bank statements sent to your address from now on. Also, have your Aunts bills forward to your home, that will give you a better grasp on her bills. I kept all bills/invoices plus a copy of the check in a 3-ring binder in case there were any questions.

Then that way, if your Aunt's children and grandchildren have their hand out for money, they would need to go through you. It will be easier for you to say "sorry, your Mom cannot afford to give you money" then for your Aunt to say that. Set up an allowance so that your Aunt has some funds for herself. If she has a lot of credit cards, limit her down to one card with a low limit, that hopefully will curb any unnecessary spending on her part.

No. You would not be responsible for your aunt's debt.

Think of yourself as a pair of hands with a brain attached; or a robot; or a mobile computer. If you accept POA you would be acting for your aunt, on her behalf, and that is all. You would not incur any personal liability for her bills, her debts, her costs, expenses or anything else.

If you want to make doubly certain, get the POA drawn up and explained by a reputable lawyer specialising in older people. You will also be able to get information specific to your state from your state's government's own website (don't get sidetracked onto commercial sites - look for one that says .gov somewhere).