I am a noncustodial parent, and the child support case has been closed/is closed. I am prepared to provide paperwork to support the aforementioned.
Can VA DCSE incarcerate me, the non-custodial parent, for child support case that is closed, and has been closed for over 10 years? I have been acting under the understanding told to me BY A JUDGE, the child support case is closed and I did have to send any money to VA DCSE.

Hmmm... It's possible a case to be closed and after that to be re-opened by DCSE.

What grounds are they trying to use against you?

My case is closed also (a case in Leesburg VA), but they still take money out of my check. I've asked why they keep taking money out of my check for an old order that was closed in Loundon County, VA. They stated to me that I still have an open case in Fairfax county that I've already paid off, but that case is still open. As long as you have an open case anywhere, they will continue to take money out of that old case that was closed. Luckily, I get a refund check for the amount taken out the next month. I have to wait a month to get the money that they took out of my check.

You need to go back to court and get a court order closing the case and then present that to your employer to cancel the garnishment order.