In his or her discretion, a justice or judge of the court having jurisdiction of such petition, by an order signed by him or her, may direct a stay of proceedings on the judgment, whether execution has issued or not, until a final decision is made upon such petition. Such stay of proceedings shall not operate to discharge or release bail or extinguish or prevent the perfecting of a lien which the petitionee has acquired upon the property of the petitioner by attachment or levy of execution.