Wyo. Stat. § 31-10-104
In the event of payment to an insured under the coverage required by W.S. 31-10-101 through 31-10-104 and subject to the terms and conditions of the coverage, the insurer making the payments is entitled to the proceeds of any settlement or judgment resulting from the exercise of any rights of recovery of the insured against any person or organization legally responsible for the bodily injury or death for which the payment is made, including the proceeds recoverable from the assets of the insolvent insurer. Whenever an insurer makes payment under the coverage required by this section which is occasioned by an insolvency, the insurer's right of recovery or reimbursement shall not include any rights against the insured of the insolvent insurer, but the paying insurer may proceed directly against the insolvent insurer or its receiver, and in pursuance of this right the paying insurer shall possess any rights which the insured of the insolvent company might otherwise have had, if the insured of the insolvent insurer had personally made payment.
W.S. 31-10-104