My Mom (88) lives with me. She is quite healthy. I cover all the expenses of the house. She pays for her supplemental health insurance. I cover co pays or whatever comes up. I used to rent my spare room out but I have mom now which is a blessing but a bit of an expense.
The second program is called Medicaid. Its the program of last resort, you must "spend down" your entire life's savings before you can get into this type of system unless you have a "State Partnership" Long Term Care Insurance plan which allows you to transition to Medicaid directly with out going through the spend down process after the initial value of the Insurance Plan is expended.
But because your mother lives with you, and all her needs seem to be met... by you... I doubt she would qualify for any these programs, or any government grant type programs either.