I don't know California laws but it's generally accepted that child support is to be paid whether or not one is working. It does come out of the family income and so if the wife is working the support should still be paid. I don't know how it's collected.
If the child support was garnished out of his check the employer is to notify the State when he quits or is fired. Tell the child support services that he says he's unemployed. They can check that out.
If your phone has a speaker option you can put it on speaker and go about your work while you wait. Or make the call when you have paper work to do. I think you do need to talk with them. They may be able to answer all of your questions.
You could also call his place of employment and ask for him by name. If they say he no longer works here you'll know that much is true.
I'm not sure what you mean by child support services. And I'm not sure if you mean that his wages were garnished by court order or if he pays thru the state per the child support order. There is a difference.
I suggest that talking with an attorney could be helpful. These are questions you can ask over the phone or many attorney's will make a one time appointment to discuss the possibility of their involvement for free. Be sure to have all court papers with you when you ask.