N.Y. Fam. Ct. Act § 474
A default in the terms of the order shall constitute a breach of the undertaking. When there has been a default the court shall cause an affidavit to be drawn, verified and filed by any person familiar with the facts. The surety shall thereupon be personally served, or served by registered mail at the address given in the undertaking or subsequent address furnished by said surety in writing, with notice of such default and shall be required to attend at the court on a day certain and show cause why judgment should not be entered on the undertaking and the amount thereof applied to the relief of the petitioner for the amount in default. If the surety appears and pays the amount in arrears the court may remit the forfeiture. Inability to serve the surety shall not be prejudicial to the renewal of proceedings against the respondent.
N.Y. Family Court Law § 474