It is doubtful he can do this, and not have to pay anything at all.
I know, about 2 months prior to my final day in court, for divorce, I lost my job. My lawyer told me I needed to hurry up and find a job as quickly as possible. He didn't even want to show up in court without me being employed once again.
At the time, I really wondered if I'd ever get the divorce over with.
I think your x is probably only hurting himself on this. If he's unemployed, the judge could possibly order him an amount to pay based on his past salary history.
I was making $140k per year before losing that job. I took another job at $80k. The $80k is what they used to plug in the formula for child support.
My lawyer warned me that I couldn't just go out and run the register at the supermarket or something. I had to find a job that reflected my past earning potential. My x's lawyer contested it, saying I could make more money. At the very same time though, they told the judge I was on drugs/alcohol, and was mentally unstable. My x wanted me to have supervised visitation with my daughters (once per month) and she demanded I give up all my parental rights.
The judge basically told her if I really am as bad as she said, how could she then think I could make more money, or hold down a job at all? She was told to pick one or the other. She picked I could make more money, and quickly lost