It is possible, if you are also paying substantially, against the arrears. You did not state how long you went without paying (and thus the amount of arrears), however and that will certainly impact your outcome. If it was more than a year, the prosecutor is not likely to drop the matter.
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For support arrearages, the typical action is to have you make payment towards the arrearages within a determined amount of time. If you make the payment, then the charges are dismissed, if you don't you go to jail. Payments now towards the arrearages may not be counted, depending on the prosecutor.
Since jail is a potential outcome, you have a right to request a court appointed attorney if you qualify for such.
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Get a lawyer, court appointed or otherwise. There are forms you can fill out with the CSEA when you lose your job. In the future take advantage of them. Yes that means reading what is sent to you from the CSEA. However if you are making payments as scheduled, and have been for a whole, I have found the agency to be quite reasonable. You need counsel though.
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