My mother who now lives with me has $11,000 in credit card debt that she can't afford to pay. What can we do?

Bonniewise, I encountered something similar when I became my sister's conservator of person and estate, following a closed brain injury. She had about $40,000 of debt. AT first, I was paying it off and struggling mightily (emotionally and financially) with it. Then, one of the credit card company representatives gently let me know I did not have the obligation to do so, and that if they got a note saying the debt was uncollectable due to my sister's permanent disability and lack of any assets, they would write it down. That's what I did. I felt bad about the actual cash the company was out (which was way less than the interest and penalties that got the bills to $40K to begin with). AND the truth was it was not my obligation AND I was using my resources to care for Ellen, as best I could, in that situation. Others may disagree with the idea of letting the bills go. But the companies do encounter this situation. Be prepared to show the paperwork that your Mom is permanently disabled on SS income; show how her income is spent (when it's in a nursing home, it's easier to show there is no money left over, but you may be able to make the case) and (unless you are her conservator), get her to send the letter in her name. Alternatively, maybe they would be willing to forgo interest and penalties and just accept minor payments toward the principal balance. Just intend that you get connected to the right person, to someone who will be personally helpful when you call. Good luck.

Is the debt still piling up or just staying the same? If it's just staying the same, good for you -- you're making ends meet now. But chip away at what you can. For example, has each and every doctor who prescribe drugs for your mom been explicitly asked for a generic equivalent that may be less expensive? Ask the pharmacist, too. Don't assume anyone will think of that on their own, unfortunately.
What will make old debt keep growing is the interest. See if you can find a lower-interest source of credit you can use to pay off those credit cards. A home equity line of credit is an example (with two cautions: if it's your home it becomes your debt, and you certainly don't want to risk losing your house over $11,000). "Secured" debt -- meaning debt with something like a house attached -- is cheaper than unsecured debt, because the collateral object is at risk. Maybe there's something else you could put up as collateral that wouldn't be so devastating to risk. Check out the possibility that a bank loan, say from a local credit institution, might be a better deal than the credit card, and try to do that in her name rather than yours.
A simple thing to do is, you can ask the credit card companies directly to lower the interest rate -- they'd rather get some payments than have your mother simply default. If you are tempted by credit-consolidation offers from other credit cards or ads from debt-management companies, be careful.
If your mom is totally dependent on you and her credit future is nil anyway, consider bankruptcy for just her. For more on all of those options, read http://www.ftc.gov/bcp/edu/pubs/consumer/credit/cre19.shtm

Stop paying on your mother's credit cards and don't have a single guilty thought! the credit card company had the opportunity to evaluate your mother's 'credit worthiness' and the ONLY reason they chose to extend credit to someone living on social security and a bit of babysitting income is because they (due to deregulation) were able to make money on bad debt. Plus, if the debt is 3+ years old, the principal was paid long ago. What's left is the (exhorbitant) interest and fees. Your mom has no assets. It's highly unlikely they'll put much effort into going after her. You will get a bunch of threatening phone calls from collection agencies. Ignore them and threaten them back. You are not responsible for your mom's debt. You have better things to do with your resources. Save them for taking care of her and of you. Please don't pay them a single dollr more than you already have. I speak from experience. My dad, in the early stages of dementia, had run up more than 15 credit cards and he was still getting card offers in the mail.

Stop paying on your mother's credit cards and don't have a single guilty thought! the credit card company had the opportunity to evaluate your mother's 'credit worthiness' and the ONLY reason they chose to extend credit to someone living on social security and a bit of babysitting income is because they (due to deregulation) were able to make money on bad debt. Plus, if the debt is 3+ years old, the principal was paid long ago. What's left is the (exhorbitant) interest and fees. Your mom has no assets. It's highly unlikely they'll put much effort into going after her. You will get a bunch of threatening phone calls from collection agencies. Ignore them and threaten them back. You are not responsible for your mom's debt. You have better things to do with your resources. Save them for taking care of her and of you. Please don't pay them a single dollr more than you already have. I speak from experience. My dad, in the early stages of dementia, had run up more than 15 credit cards and he was still getting card offers in the mail.