Any person who is, or becomes, a recipient of old age assistance, aid to the permanently and totally disabled or intermediate care facility assistance while at a hospital, home for the aged, nursing home, rest home, convalescent home, residential care facility for adults, or similar facility, or an elderly or disabled person, who lives in a multiple unit rental dwelling which is fully or partially subsidized by the United States Department of Housing and Urban Development or the United States Department of Agriculture’s Farmers Home Administration, is the responsibility of the county in which he last resided before entering such institution.