Are there any assistance programs that will help pay for elderly debt?

Unless you can have a system to intercept all telephone calls and outgoing mail I do not see what you can do even if you have POA. The main thing is to protect yourselves to make sure that you have no responsibility, and to make sure statement are filed with equifax, transunion, and experian -- usually one call is enough to all three. I do not see what you can do other what I have stated to protect yourselves and your father.

My husband and his brother have DPOA for his mother, who is now in assisted living. We had to put a freeze on her credit in order to protect her from more scams and prevent her from getting more credit cards. Her only income is SS. Yet she still sends in credit applications trying to go behind their backs and get credit cards anyway.

There are several ways to approach this. I am going to try to give you ethical advice here, which would not benefit your position, but which should protect you and your brother.
1. How bad is this? Has your father racked up thousands in debt that need to be paid off? What is the amount? If it is a minor amount (under 5000) you might ignore it if he has no assets and do not mind getting badgering collection calls which you will have to send a registered letter requesting that they be stopped to any agency who calls you.
2. Does your fathers assets outnumber his debts? If not, you should consider filing bankruptcy for him. You will need to meet with an attorney, so not consider handling this yourself.
3. Immediately call up one credit bureau and tell them that you are your father's guardian and that he is no longer capable of taking out loans which can be paid off. However, it sounds like the credit bureaus already know this. Still, you need to stop his ability to taking out loans -- particularly from those who take advantage of the elderly with outrageous rates and scam offers.
4. One thing you need to determine is this -- how liable are you and your brother for your father's actions now that you have POA? I do not think you do but you need to meet with a trusted family lawyer to know your rights and liabilities here, even for a quick initial meeting that you will not be charged for.
Only use a trusted family law attorney. You can also get low cost or free legal advice by calling your local bar association.
Be aware that if your father goes into bankruptcy, he can continue to take out loans which will not be covered under the initial filing.
But, as someone has mentioned, if he has no assets, and if lenders are targeting him unscrupulously, and you and your brother have no responsibility for his debt (please check your state law about this if you have POA), you can just ignore it. I would meet with a lawyer however.

Yes, my brother and I have POA and we are going to talk with the bank and lending company about not giving him anymore loans. It's just overwhelming trying to deal with the amount of debt he has accumulated. Yes his only income is Social Security. And he really is too sick to get a part time job to increase his income.

Only thing I can think of is bankruptcy.

No, I doubt that there is. How serious is the debt? You may want to get with a financial counselor and work through it. How old is your father? If he is living only on SS, creditors will not be able to garnish payments from it. If your father were to die, creditors could file claims against the estate. If there is not enough money in his estate to cover debts, they cannot go after the heirs to collect it.

I hope you can help him not accumulate any more debt.

Perhaps you need y to get guardianship? Do you have poa?