The best way to respond to the non-custodial parent's request to modify his or her current child support to $0 is to simply opposed the petition where the court sets child support based upon county guidelines on each parent's net monthly income per an income and expense declaration submitted to all parties and the court.You may need to consult with a family law attorney to assist you in the opposition. Potentially the court could mandate the non-custodial parent to get a job or simply set the monthly child support at a certain amount regardless of no claimed job.