Does a debtor have the right to correct an error in a court order?

I recently learned about a decision of the Supreme Court, according to which the State Treasury, being a debtor in the case, has the right to file an application to correct an error in a court order. Previously, courts would return such applications without consideration, believing that the applicant was not a party to the case. Now I want to know: does this rule extend to other situations where the debtor was not a participant in the court proceedings but is specified in the enforcement document?