There certainly could be a problem if a person owes money on a home mortgage and applies for Medicaid. Medicaid won't let the recipient divert income to keep up the mortgage payments; all the income must go to the nursing home (less a personal needs allowance, MMMNA for the spouse, if any, etc.).
I don't know of any solution, really. Usually people are elderly by the time they apply for Medicaid and have paid off the house by then. If indeed there is a mortgage, they may have to sell the house or arrange for children to pay the mortgage if they want to keep it.
I have lot's of medicaid info at http://www.medicaidsecrets.com/
