If non-custodial parent owes over $12,000 in back child support to custodial parent and decides not to file tax return, what happens?

[Heather14]

If you are required to file a tax return and do not file you may be required to pay a fine or even face criminal charges. Per the IRS: Taxpayers who owe tax, and failed to file and pay on time, will most likely owe interest and penalties on the tax they pay late. To keep interest and penalties to a minimum, taxpayers should file their tax return and pay any tax owed as soon as possible.
If you owe back child support, any tax refund may be offset either by the IRS or by your state's Department of Revenue, but it is in your best interest to file the taxes. 

Please see the following IRS link for more information: https://www.irs.gov/newsroom/important-facts-about-filing-late-and-paying-penalties