if your on temporary assistance and you get back child support does the state take that?

Here’s the story my ex has never paid child support on our daughter. I ain’t push this, but he owes 7400 dollars to her. Well I’ve been on government assistance *tanf* for over a year because even tho I work I also do community service for the tanf because I do not make enough from my paychecks. I only get 100 in tanf a month. Well the state has decided to take it into their hands and get her dad since he owes so much and has never in her life paid. She’s 7 years old. He hasn’t been around for her or done anything for her. Ever. So I don’t feel the need to cancel it. This is court ordered child support also. Also I’m 22 so I had my daughter very young. Now I’m wondering since he has to start paying back child support does the state take that or do I have to give it to them or what happens? I doubt he’ll ever pay it but incase he does , can somebody tell me what I’ll need to do? I’m not sure how any of this works. Btw he only owes 150 in child support each month. That’s the agreement. Would they send me the recent and back child support when the take from his checks?