This involve Illinois.
And its more about curiousity rather than a particular case (although it may come in handy later).
From the way I understand Illinois law regarding child support if a NCP (usually a father) is not employed, the courts may require him to participate in a job search program and report his efforts back to the court similiar to the way unemployment agencies work. Essentially, requiring him to find a job.
Is it possible to have the CP (usually the mom) do the same thing? If she is not working, it seems like it would be only fair to require HER to do something to locate work and help support the child especially if child support and state aid were her only forms of income.