Usually, yes. In most circumstances, she could move into a nursing home and qualify for Medicaid(called Medi-Cal in California) coverage of nursing home costs while still keeping her own house, as long as her other assets and income are below the state's Medicaid eligibility limits. This house exemption only applies, however, if her equity in the house is below the level set by her state. These state equity levels range between $500,000 and $750,000. Also, this exemption applies only to her primary residence.
While she lives in the nursing facility, family members or others may live in the house without this affecting her Medicaid eligibility. But if the house is rented to anyone, the rent money must go toward the cost of the nursing home.
Although Medicaid will not force her to sell the house, Medicaid does have a right to be reimbursed out of the value of the house when she dies, for the entire amount it winds up spending on her nursing home care. Medicaid accomplishes this by making a claim against her estate. To help ensure that Medicaid can collect this reimbursement, it may place a lien on the house while she's still alive. As long as she lives, however, Medicaid will not seek to enforce the lien.
In some states, in order to keep the house, a Medicaid recipient entering a nursing home must state on the nursing home admission form that she intends to return home -- even if, in reality, this is highly improbable. In other states, there is no such "intent to return home" rule.
To find out what the home equity limit is in her state, and to learn whether there is an "intent to return home" rule, check with the Medicaid office for that state. You can find the state office by going online to any search engine and entering Medicaid and the name of her state. Or you can call the Eldercare Locator toll-free at (800) 677-1116 and ask for contact information for that state's Medicaid office