Why would you believe that a care home determines whether or not someone remains on Medicaid? There is a state or county official that does that, not a private party. The care home may be telling her what they think is true. Doesn't mean it is true. But the state or county official also won't tell you anything since your friend is legally competent.
You said she is an SSI recipient. But then you also referred to her as getting SS benefits. Answers would be different, depending upon which program you are referring to. In some states, all SSI recipients get Medicaid for the months they are on SSI. Then it is a federal decision that allows the Medicaid.
I think she has too many problems to try to solve in this forum. She is a legally competent adult. What does she want to do?
