Upon presentation by the county treasurer to the county commissioners, either for purpose of accounting or settlement as by law required, or otherwise, of statements of account and balance sheets in which is disclosed an item or items of assets that amount to fiction, represented by bank accounts or securities that, because of bank failure, robbery, theft, embezzlement, or otherwise, are nonexistent, worthless, or unenforceable, then the county commissioners, Judge of the District Court and District Attorney are hereby authorized, by quasi-judicial proceedings, the Judge of the District Court presiding, to make a determination of the status of such item or items of assets; and upon first finding that such item or items have been carried on the treasurer's accounts fifteen years or more without realization or abatement, they shall then proceed to further determination for purpose of correcting said accounts to procure a liquid condition. If, after first finding said fifteen years to have fully run, they find such fictitious, nonexistent, or worthless and unenforceable asset to be not identifiable as an asset of a corresponding fund liability account, they shall so state, and thereupon, by decree and order direct that the county treasurer henceforth apply and determine percentage, not exceeding twenty-five (25) percent, of the penalty and interest on delinquent taxes, as collected by him, that would otherwise be apportioned to the county under the statute, to the liquidation of such fictitious, nonexistent, or worthless asset, and to so continue until such account is closed by such liquidation.