Mich. Comp. Laws § 418.651

Sec. 651. Nothing in this act shall affect any existing contract for employers' liability insurance or affect the organization of any mutual or other insurance company or any arrangement now existing between employers and employees, providing for the payment to the employees, their families, dependents or representatives, sick, accident or death benefits, in addition to the compensation provided for by this act. Liability for compensation under this act shall not be reduced or affected by any insurance, contribution or other benefit whatsoever, due to or received by the person entitled to such compensation. The person so entitled, irrespective of any insurance or other contract, shall have the right to recover the same directly from the employer; and in addition the right to enforce in his or her own name in the manner provided in this act the liability of any insurance company who may have insured, in whole or in part, the liability for such compensation. Payment in whole or in part of such compensation by either the employer or the insurance company carrying the risk shall be a bar, to the extent of the payment, to recovery against the other of the amount so paid.