I'm owed over $15,000 in child support, what happens if the NCP doesn't file taxes for more than two years?

If the deadbeat parent does not file a tax return with a refund that can be seized, you cannot collect from taxes.  You have to take further steps with the local agency that enforces child support orders and seek some way to garnish wages, etc,

FYI ... they could be filing a tax return but not have a refund to be grabbed on purpose ... nothing you can do about that ... seek alternative options thru the courts.