I believe any award due New Jersey should go into the unemployment fund to extend benefits rather than toward principal reduction because a significant number of homeowners are engaging in tactical defaults – they can meet payments but default anyway as a business decision because they mortgages are under water. Reducing their principals may or may not act as an enticement to continue payments.
However, recipients of aid to reduce principal could be made liable for any aid received if they default afterwards. In other words, it could be a voluntary program where the recipients enter into a bond with the state agreeing to hold on to their mortgages.
Extending the unemployment benefits on the other hand helps who have truly lost the ability to make payments.
These above are just opinions. Ultimately, it is the current state government which must make the proper decision.