Upon payment in full to any public depositor on any claim presented pursuant to § 2.2-4403 or 2.2-4404, the Treasury Board 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 ratably with other depositors. Any sums received from any such distribution shall be paid to the other qualified public depositories against which assessments were made, in proportion to such assessments, net of any proper payment or expense of the Treasury Board in enforcing any such claim.