What happens if the final divorce papers are not signed by the Petitioner but are signed by Respondent after 30 days of the Judge finalizing the divorce?

If the judge has signed them, the parties' signatures are not required. If one party has prepared the decree following the judge's oral pronouncement, and if the other party fails to sign the proposed draft of the decree of divorce so that it can be submitted to the court, then the drafting party should file a "Motion to Enter" with a copy of the proposed decree attached to the motion and seek a hearing on the motion, and at such hearing the Court will enter a decree with or without signatures.