If you apply for any, ANY, state aid such as medical cards, food stamps, child care assistance, housing assistance, WIC, they will require him to pay child support, you will still receive the benefit but they will make you sign a statement giving them the authority to file for support for your children. You should receive child support, they are his children too and it is his responsibilty. If you ever want to be able to afford extras like sports, dance, college, occassional snack food, etc...you will need that money.
If he is abusive to you and you are afraid that if he is ordered to pay child support he will try to hurt you or the children then there are some laws around to offer you protection but your local child support office could give you more details.
We live on SSI and are raising some of my granchildren. The kids fathers don't see them, they just don't care enough I guess. The court ordered child support and so our local child support office handles the finding the fathers and contacting their employers. The child support is taken out each payday and the employer sends/online transfers it to the child support office. The dads don't actually ever see the check. It is automatically deposited onto a debit card that I use for many things.
One of the dads sends money for Christmas and Birthdays too but it is extra and doesn't count towards the regular payment. Also he carries his daughter on his insurance. It also is an extra he does and it does not count as child support. It's a voluntary thing for him to do and even though we have medical cards on the kids we appreciate him making the effort.