Child support confusion

by confused
(ny)

My wife and I had a dispute over moving out of state. She wanted to be near her family, and I needed to move for work. She refused to go, so we became estranged. We have 4 boys and during that 6 month period, she filed for food stamps in New York. I guess automatically the state starts a child support case. However, she never followed up and only collected food stamps for a few months before we got back together. My question is being that she never followed up and, we are back together, and she is not getting welfare does the child support thing go away.