This is a great question. If your loved one resides in an assisted living or independent apartment and becomes unable to pay the bill, and if family cannot step in
to cover the cost, he or she will be asked to leave. If he or she does not leave, the facility may begin the eviction process.
That said, there are some assisted living facilities that accept Medicaid, so it is definitely worth the effort to try to find one, but they are few and far between and waiting lists can be long. Even so, a facility's costs can exceed the Medicaid reimbursement so there can still be out-of-pocket expenses although they should be much less.
Most people choose to spend what funds they have on home care or an assisted living facility until the money dwindles to the Medicaid maximum. Then they apply for Medicaid and transition to a nursing home. New York is the only state I am aware of that offers a second option which is Medicaid-covered home care. With this option a Medicaid applicant can transfer assets to an adult child for example and still qualify for home care. If your parents reside in New York, you'll want to look into this option.