No. Even under Ohio's Assisted Living Waiver, Medicaid pays for the care-services portion of an assisted living stay, not room and board. Families cover room and board out of income, Social Security or other private funds.
The detail behind the program
This is a distinction almost every family misses on first contact with the system, and it changes the math significantly. A community can hold an Assisted Living Waiver provider agreement and still require the resident to privately cover rent every month, with Medicaid only offsetting the care-services charges. When you ask a community whether it 'takes Medicaid,' ask the more precise question instead: does it hold an Assisted Living Waiver provider agreement, and how much of the total monthly bill would still be the family's responsibility if your parent qualified?