Oh ho, so we have someone thinking someone somewhere is getting something she doesn't think they deserve. Okay. If there is a total calculation of income and resources for this household, and the administering officials find that the household income is still low enough, the household resources are not great enough to keep this group from being eligibile, yes, they can still get assistance, particularly with health care for children.
As far as the mother not working, after a certain point, with a certain number of children in the family, the cost of child care is going to be almost greater than anything she could earn, so it may make good financial sense for her not to work.
The income and means for public assistance recipients are checked very regularly. If you feel there is fraud going on in their receiving assistance, or think they have other sources of income they are not reporting, you are welcome to call and report it, and the case will be re-verified. But just because you do not feel that these people do not deserve something is not an indication they are not entitled to it.