Mich. Comp. Laws § 600.2655

Sec. 2655. Whenever any person becomes security for costs for another, in any court in this state, whether such security is required by law to be given, or is required by order of the court, in case the opposite party in any such action recovers final judgment for costs against the principal, thereupon judgment or decree may immediately be entered, as well against such surety as against such principal, and execution may issue against such surety, in the same manner as if he had been himself a party to such suit.