It is possible for someone to be self-employed and not get 1099’s. Someone can be self-employed and not be receiving $1,000 a year from one entity.
Additionally, he can be unemployed and have someone else supporting him.
Also, how would the State even know that he is not paying child support unless his ex-wife reports him (and she may be reluctant to do so, or there may be halachic issues involved)?
Also, the issue could be that he managed to get away with making a (unfair) deal that he wouldn’t have to pay child suppport in the first place – maybe it was the only way he would agree to give a Get even though the Beis Din said that he should.
There are many ways that a person can be negligent in his responsibilities if he really wants to be (I am not talking about someone who really, really is trying his best, and is just not able to).
Of course, it will be hard to get to the bottom of it in any case, but I think it is kidai to at least ask. The answer may provide a red flag that would be worth looking into further.