The answer depends on two factors: how the deed is titled and whether your state’s Medicaid estate recovery program seeks recovery from non-probate property.
First, if you are all joint tenants with rights of survivorship, then when each owner dies, ownership passes automatically to the surviving owners without the necessity of probate. However, if you are tenants in common, then each owner’s interest will pass to their estate upon death and have to be probated. In the latter case, your parents’ share of the house could be subject to claim by Medicaid to recover the state’s costs of providing for their care.
If, on the other hand, you are all joint tenants, then there will be no probate when your parents pass away, and the state may or may not have a claim against your house. Some states’ Medicaid estate recovery programs seek reimbursement from non-probate property, and others do not. A local elder law attorney can advise you on whether your house would be subject to claim in your state and, if so, what steps you might take to prevent this from occurring. You can find a qualified attorney in your area here.