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What can I do with a physical stock certificate for a now-mutual company?
I found the following on a stock to mutual conversion for insurance firms for Ohio. Pulling from that link,  Any domestic stock life insurance corporation, incorporated under a general law, may become a mutual life insurance corporation, and to that end may carry out a plan for the acquisition of shares of its capital stock, provided such plan: (A) Has been adopted by a vote of a majority of the directors of such corporation; (B) Has been approved by a vote of stockholders representing a majority of the capital stock then outstanding at a meeting of stockholders called for the purpose; (C) Has been approved by a majority of the policyholders voting at a meeting of policyholders called for the purpose, each of whom is insured in a sum of at least one thousand dollars and whose insurance shall then be in force and shall have been in force for at least one year prior to such meeting.  and Any stockholder who has assented to the plan or who has been concluded by the vote of the assenting stockholders, and any stockholder who has objected and made demand in writing for the fair cash value of his shares subsequent to which an agreement has been reached fixing such fair cash value, but who fails to surrender his certificates for cancellation upon payment of the amount to which he is entitled, may be ordered to do so by a decree of the court of common pleas for the county in which the principal office of such corporation is located after notice and hearing in an action instituted by the corporation for that purpose, and such decree may provide that, upon the failure of the stockholder to surrender such certificates for cancellation, the decree shall stand in lieu of such surrender and cancellation.  Since they successfully became a mutual insurance company, I would guess that those stocks were acquired back by the company, and are leftover from the conversion. They would not represent an ownership in the company, but might have value to a collector.