In California about the only welfare/services available to a single adult would perhaps be general welfare (a check), food stamps and possible Medi-Cal coverage. I'm not sure what's available in regards to subsidized housing, if anything.
With kids, it can start from the get-go with "free" prenatal care and delivery. All children, legal or not, are required to attend school and they most likely qualify for free breakfast, lunch and in some cases, after school care. Kids can be enrolled in Head Start programs. There's WIC, food stamps (based on the size of the family), subsidized housing and health care programs. I can't even remember the names of some of programs California has besides MediCal. One is called Healthy Families (or something like that).
What I'm getting at is that an adult, with no kids and who is under 65 years of age, just doesn't qualify for much assistance. If you have children, however, then the floodgates open.
The children need an education, the children need health care (and we want the children to have healthy parents, don't we?), the children need to eat, the children need a house/apt. to live in, etc. The fact that the money/services also benefit their parents is irrelevant.
(Am I making any sense? I feel like I need more coffee.)
LOL. Yeah, I know that feeling.