On the death of a person receiving or who has received assistance under the provisions of this chapter, and whom the board has previously found, under section 230.25, is able to pay there shall be allowed against the estate of such decedent a claim of the sixth class for that portion of the total amount paid for that person’s care which exceeds the total amount of all claims of the first through the fifth classes, inclusive, as defined in section 633.425, which are allowed against that estate.