They are on Medicaid and will absolutely report the births because it's more government assistance, especially before age 5 when they can get WIC.
It's actually easier to raise children if you're poor because of the benefits cliffs but WIC in particular is actually very generous with the income limits. It only takes a couple kids (they don't all have to be under five to count) to hit a cap that exceeeds local median wages.
Not entirely. If I'm on the jury, no amount of evidence is getting a conviction from me. They just have to survive long enough to get that far.