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In general, a landlord in California does not need a reason to terminate a tenancy. A month-to-month tenant who has lived in rental property for at least a year may be asked to leave at any time by giving written notice at least 60 days before the end of the rental period. Cal. Civ. Code, Section 1946.1. Living in a house for an extended period of time does not give a person any more rights than a tenant who has lived there for one year and one day. Being elderly or disabled does not confer any rights above and beyond other tenants in most cases, because 60 days is usually plenty of time to move. She would not have to pay them a penny. If she serves a notice and they don't leave, she can go to court and have them evicted.
However, there could be exceptions if your mother lives in a city with rent controls. If that is the case, please let me know which city so I can do some research for you. Many cities still allow a landlord to remove a tenant in order to have a family member move in, but an $85k buyout is beyond ridiculous. They don't own the property. I honestly question whether the person who sent that offer is a real lawyer, because I don't see how he could be if presented with the same facts you gave me.
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