If the judgment debtor shows the circuit court that an appeal from the foreign judgment is pending or will be taken, or that a stay of execution has been granted, the court shall stay enforcement of the foreign judgment until the appeal is concluded, the time for appeal expires, or the stay of execution expires or is vacated, upon proof that the judgment debtor has furnished the security for the satisfaction of the judgment required by the state in which it was rendered. If the judgment debtor shows the circuit court any ground upon which enforcement of a judgment of any court of this Commonwealth would be stayed, including the ground that an appeal from the foreign judgment is pending or will be taken, or that the time for taking such an appeal has not expired, the court shall stay enforcement of the foreign judgment for an appropriate period until all available appeals are concluded or the time for taking all appeals has expired, upon requiring the same security for satisfaction of the judgment which is required in this Commonwealth, subject to the provisions of subsections J and K of § 8.01-676.1.