(a) Unpaid charges accruing after January 1, 1978, and owed by a parent for the support, maintenance, and treatment of a resident are a claim in favor of the state for the cost of support, maintenance, and treatment of the resident and constitute a lien against the parent's property and estate as provided by Section 533.004, but do not constitute a lien against any other estate or property of the resident.
(b) Except as provided by Section 593.081, costs determined under Section 593.073 constitute a claim by the state against the entire estate or property of the resident, including any share the resident may have by gift, descent, or devise in the estate of the resident's parent or any other person.