If someone other than the employee or the State causes an injury for which work-related accident leave is taken under this subtitle, the State, as employer, after giving written notice to the employee, is subrogated to the rights of the employee to the extent of any compensation paid or owed under this subtitle. The State, in its own name and for its own benefit, may bring an action or join in an action if: within 90 days after the employee receives notice from the State under subsection (a) of this section, the employee fails to: enforce the claim against the person causing the injury; or give written notice to the State of an intent to do so; or within a reasonable time after giving the State notice of an intent to enforce the claim against the person causing the injury, the employee fails to take action to enforce the claim. An action brought by the State under this section is not a bar to any other claim related to the injury.