Subject to the limitations in this section, the Treasurer shall pay a unit of the State government for a loss that is covered under § 9-105 of this title, without regard to whether the unit is funded wholly or partly from general, special, or federal funds. The unit of the State government that had State property at the time of its loss or damage and the Treasurer jointly shall determine the value of the property. The Office of the Attorney General shall determine and certify to the Treasurer the value of a liability claim against the State. The Treasurer may not pay from the Fund any money for loss or liability in excess of the value certified under this subsection. Notwithstanding any other provision of this title, the 1st $1,000 of value of each loss, damage, or liability occurrence of a unit shall be paid from its appropriations in the State budget unless, on recommendation of the Secretary of Budget and Management, the Treasurer reduces the amount.