Such court may, however, without notice or the appointment of a guardian ad litem, proceed on such petition in accordance with the preceding section and with like effect: Provided, That any person whose interest may be affected by the proceedings under this section, or who in any case shall have been proceeded against by publication, or the personal representative of any such, shall have the same rights, as to a rehearing, that may be allowed by law to nonresident defendants in actions at law or suits in equity.