Upon payment in full to any designated state depository on any claim presented pursuant to this article, the State Treasurer shall be subrogated to all of such depositor’s rights, title, and interest against the depository in default or insolvent and shall share in any distribution of such defaulting or insolvent depository’s assets in the same amount as would have been received by the public depositor ratably with other depositors. Any sums received from any such distribution shall be paid to the other designated state depositories against which assessments were made, in proportion to such assessments, net of any proper payment or expense of the State Treasurer in enforcing any such claim.