Parents are legally required to support their minor children. There is not a method to waive that right. However, frequently the child support amount can be adjusted up or down based on specific circumstances. In doing so, the court agreement must state the specific reasons the child support is being deviated to zero. Most courts will look this over and determine if it is reasonable.
If your ex is receiving a court notice on back child support, then an actual order when of record. This means that the court does not have a proper agreed entry or order regarding the support agreement that you two made.
I strongly suggest that you seek an immediate consultation with counsel. You will want to take with you ALL court orders, agreements, etc. This matter needs to be reviewed and it needs to be determined what is actually of record and then how to correct it.