(c) If an employee who shall be disabled, or his widow or children receive any compensation or payment from the county for specific loss, disability or death under the Workers' Compensation Act or Workers' Occupational Diseases Act, the disability benefit or any annuity for him or his widow or children payable as the result of such specific loss, disability or death shall be reduced by any amount so received or recoverable. If the amount received as such compensation or payment exceeds such disability benefit or other annuity payable as the result of such specific loss, disability or death, no payment of disability benefit or other annuity shall be made until the accumulative amounts thereof equals the amount of such compensation or payment. In such calculation no interest shall be considered. In adjusting the amount of any annuity in relation to compensation received or recoverable during any period of time, the annuity to the widow shall be first reduced. If any employee, or widow shall be denied compensation by such county under the aforesaid Acts, or if such county shall fail to act, such denial or failure to act shall not be considered final until the claim has been adjudicated by the Illinois Workers' Compensation Commission.