My mother needs a loan to pay out her credit card debt. She has fallen behind because of the problems at work and not receiving as much money as she used to.
There is likely no source of loan for this purpose. If you change the question to read "Who would be willing to lend me money when I can't repay the people I borrowed from before?" - you can clearly see that that answer is likely no one.
Possibly bankruptcy is the only way to discharge the debt. You may wish to speak to a bankruptcy attorney. You will have trouble then borrowing in the future, but you may be able to get your current debts discharged or restructured to something you can afford. Good luck.
There are no easy fixes to excessive debt, particularly credit card debt. I would be very careful about obtaining a new loan to pay off credit cards as it does not fix the root cause and may compound the problem. Using a home equity loan may place your home at risk as you are exchanging secured debt for unsecured debt.
Work on paying off your higher interest credit cards first and move high interest balances to lower interest credit cards if possible.
Stop using your credit cards, cut your spending for non-essentials, and increase your income by locating additional employment. (as painful as this sounds, non-essentials would include those items not necessary for living, such as cable TV, coffee, cell phone, DSL, etc) Consider taking a class on how to take control of your finances such as the Dave Ramsey Financial Peace University.
If her income went down and it is not going back up any time soon, you have to see if by reducing her expenses she could sustain her living. John's advice is right on the point, borrowing money to pay off debt when your income is going down is not a sound way to solve problems. If she has assets that she can sell that would help. In addition to cutting expenses you should sell non essential stuff, a garage sale would help. Don't be afraid to consider bankruptcy if by cutting her expenses she can maintain her living but she does not have a chance to pay off debt. Dave Ramsey has a service that he sells that counsels people away from bankruptcy. Most bankruptcy attorneys disagree with his advice. I would only use Dave Ramsey for his focus on cutting expenses.
You can also contact the credit card companies and tell them to freeze/cancel the accounts and place them on a 5 year pay off schedule using the minimum monthly payment amount. This will usually drop the interest rate on the card debt to 5% or less. The downside is that the credit cards are no longer available for use.