Once a Medicaid recipient leaves a nursing home, do they revert back to Medicare?

That depends on the situation, and where the patient lives. Medicaid, in some states, will pay for some in-home care, but not usually around the clock care. Some states don't pay at all. Likely, Medicaid would remain the medical insurance, however, unless the patient has gotten an infusion of money that would disqualify him or her. You'd have to check with the Medicaid people in the state covering the person now. Yes - it's a Federal program, but it also is a state program. It's variable and can be complicated, depending on where people live.
Carol