The only non-hospital inpatient care Medicarepays for is a very limited amount of skilled nursing facility care while recovering from an illness or injury following a hospital stay. It doesn't cover any of the cost of residence in an assisted living facility.
In some states, though, Medicaid, can pay for assisted living in certain participating facilities. If the state Medicaid program where your mother lives does cover some assisted living, then the question is whether the facility where your mother lives is approved for Medicaid payment and participates in Medicaid. The easiest way to find out is to speak with the administrator at the assisted living facility. If the facility does participate in Medicaid, your next step is to see if your mother qualifies for Medicaid, which she can do only if she has very low income and assets. To see about the Medicaid eligibility rules for assisted living in her state, you can go to the Medicaid information page at the federal government's Govbenefits web site.
If your mother's state Medicaid program covers assisted living and your mother could qualify for it, but the facility where she now lives doesn't participate in the program, you might want to consider another facility that does. Medicaid can pay the full cost of assisted living, and over the years that could amount to a lot of money.