It would be a little tricky, but you could probably do it. I have dealt with this in the past. Obviously, child support is for the child and not for the parent. Although child support payments are guided by statute, parents are able to stuipulate to other reasonanble arrangements. You could enter into an agreement with the other parent stating that you are not responsible for arrearages. One problem is going to be consideration. Why would the parent agree to this? Does the child benefit at all? In addition, if the parent/child are receiving any public assistance this is not going to get the paying parent off the hook.
I don't agree. In my experience, you will hardly ever be allowed to simply waive support, either past due or ongoing. Support is statutorily calculated, and the only legal way (note, I said legal - that does NOT include an incompetent judge simply ignoring the law or not reading the pleadings) to avoid support or waive it is to provide a compelling justification to the court. Your being unemployed and not getting the support modified as soon as you became unemployed is not a justification.
This answer is not to be considered a response to a specific legal issue in a specific jurisdiction - it is to be considered only a general response to a hypothetical scenario posed by the questioner. For specific legal advice, please consult with a licensed attorney in your jurisdiction.