CPS is Child Protective Services. There are also adult protective services, by whatever name, for adults who are unable to care for themselves, which is likely the case for the age 18+ people here. The notoriety of the family at least means that there are people who will help them get whatever services are available, which (almost) certainly would include Medicaid, since they don't have jobs or income. I suspect shrinks and social workers will volunteer their time just for a chance to work with such an unusual case. They have relatives that apparently are willing to pitch in. And media attention makes it easier to raise money for them.
It is a tragic commentary, though, on our system that there could be any question about how their treatment will be paid for. In any other First World country with universal health care, no one would even think to ask.