Your mother's proposal is fraud.
Once your mom liquidates her assets by transferring them to you, she'll get on a Section-8 list if her income is less than like $26,000-30,000/year. In some areas, the waiting list is long, and prioritized for families. If she falsely reports that she doesn't own her home, she'll get disqualified for lying. If she transfers the home to you and rents it at a below market rate, she is falsifying her application by not reporting income.
What happens next is that she will need to enroll in Medicaid. Medicaid does a multi-year lookback, and they will notice that you bought her house for $1. Once that happens, the Feds and the local Social Services department will be looking to you to pony up for the housing, food, and medical benefits. Best case scenario, you're writing a big check for money you don't have. (ie. You'll be paying alot of taxes on the house sale) This is also a crime.
The best thing that your mom can do is to just sell her house, spend down her money on rent and living expenses, and enroll in safety net programs if and when she needs to. She should be able to find a good apartment for seniors that has rent linked to income. It's nice that she wants to leave some money to you, but committing a crime to do so is a not-so-good idea.