You are clearly a very good daughter to do so much for your parents. Please don't forget that you have only one life, and if you use it up on caring for others, even your parents, you won't get a second shot. My first advice is to have them (not you) get in touch with the state agency that handles their type of issues. This may take some of the burden off of you, and I'm sure they'd rather take on as much responsibility for themselves as they can. From this point on, I'm going to address my response to your parents, not you, since this is their life and not yours.
Mom and Dad, from a credit perspective, it is quite likely that a credit check will be part of the application process for places such as an assisted living facility. Even if you get past the application process, you could have a tough time paying to stay in one of these places. Adult care facilities can cost from $32,000 to $73,000 or perhaps even more per year. It depends on the level of care needed. If your daughter ends up as a guarantor for any payments, you can expect that her credit will be checked also.
You may have lower-cost options. If you meet the income requirements, you may be eligible for the Department of Housing and Urban Development's Section 202 Supportive Housing for the Elderly Program. This program provides affordable housing with supportive services for the elderly. To be eligible, occupants must be very low-income with at least one person who is age 62 or older. You can learn more about the program on the HUD website. You should also research Medicaid options for help in paying for your assisted living care. Websites such as PayingForSeniorCare.com also have a lot of information on the costs of senior care.
Ruth, while it is true that your parents' income is legally exempt from garnishment by collectors, ignoring this problem is not a good long-term solution. I recommend that your father communicate with his creditors, and let them know that he is unable to pay, has no plan to pay, and is living on a fixed income from Social Security and other benefits. He also needs to watch the mail for any correspondence from collectors. If a collector decides to sue and sends a summons notice, your father will need to appear or submit the requested documents to the court. He should bring the lawyer that he consulted if he is required to appear in court. He will probably win the day, but he will still have to deal with the judicial system to do so.
Avoiding court altogether is a better way to go, and his odds of doing that will increase if he communicates with his collectors and treats them with the respect they deserve. After all, no one likes to be ignored.