Legal Question in Wills and Trusts in California

So long as the house remains her primary residence (and this is possible even if she's in a nursing home so long as she maintains her intention to return when able) the home is an exempt asset. However, if she becomes eligible for Medical to pay for her nursing home, they most likely will attempt recovery after her death. I don't think the joint tenancy (hopefully, it is joint tenancy, and not tenants in common) would prevent that, but you should consult an expert on Medical eligibility and recovery to be sure.

The nursing home cannot make your mother sell her house to pay for their services. If she requires skilled nursing care, they will charge for their services and it will be up to your mother to pay for the services. Whether she will have to sell her home for the money to pay for the services is her choice. If she does not pay the facility, they will ask her to leave and could sue her for the monies owed. If they prevail, they could record a lien against the property. But, unless your mother signs a Deed of Trust giving the facility the right to foreclose against the property, they cannot sell the property.

The real issue, however, is whether or not your mother will require Medi-Cal to pay for medical care. If yes, the State can force a sale of the property following her death. The Quitclaim will probably not protect the property from the State's lien power.

Your mother should consider some more advanced estate planning now, if she wants to preserve her home for you.