any woman of a child making application for public assistance must provide birth records for that child and make a paternity declaration. participation and co-operation in establishing paternity is a requirement to receive benefits. participation and co-operation in pursing and establishing child support is also a requirement.
i can't speak to how workers in states that have polygamist cults are trained to handle their caseloads but i can tell you how we handled the ones that practiced similar relationships/welfare fraud in our county-
mommy came in and applied for the most recent kid-we requested the bc, if they claimed no bc because of their religous practices (always claimed it was home birth and no doctors because they did'nt trust them) we required that they bring their bible record (our group recorded births in the bible), we compared the new copy to the old to see if it was consistent to the families existing copy (and not a new one created for this kid)-and affadavits from whomever was present when the child was born. we had them do the paternity paperwork-and it was incredibly detailed, if you don't know who your baby's daddy is you fill one out on every man you had sex with around conception time and give very intimate details of who, when, where, duration, identifying body characteristics

....then all those men were called in for paternity testing (and the men were more often the best source in these groups to get info from-they did'nt want to get tagged for a kid not their own). the other thing we had going for us was we kept all the cases within one unit-and with just a couple of workers covering them so they were intimatly aware of the family dynamics. we had family trees we had created using information in each of the cases so we could see if someone had multiple kids by the same man so we could pull him in for a paternity test. had index cards with info on who was at a given address so if someone reported that their 'neice' came to live with them we could see if in actuality their 'neice' was their live in so's daughter. it took hellacious organization and cooperation between the caseworkers but it prevented allot of fraud from being successfully perpatrated.
in reality-the bulk of fraudulent polygamist (religious based) welfare cases are done by virute of having dad live outside the home for legal purposes (dad spends one nite with each family but claims another legal residence-just a schill house used by the men for this purpose). the dads are reported to the agency BUT these groups are very skilled at ensuring that individual members appear to have no income or assetts. the companies that are owned are owned by their churches-and as such they can structure the situation such that it appears a father has no resources to attach to. in some states the courts are proactive and take action against fathers who fail to support their children, but the usual legal avenues-property and wage liens, revocation of professional licenses does'nt carry much of an impact when a man has none of his property in his own name, no wages ('the church provides for my needs'

) and likely no profession that carries a licensing. courts don't want dead beat daddies to sit and rot in jail-the kids get no money and the taxpayers are now paying for the mommies, the kids AND the daddies.
the last issue is, even if someone is forthcoming and honest about their polygamist husband, and even if he's working a real job-the amount of child support that would be captured from an average man (in the professions these practicers commonly work in) once divided among all the moms and the kids would have little or no impact on their still receiving benefits. ya gotta figure if someones got 20 kids with 10 different wives, even if their gross pay is say $5000 per month-IF the courts were to order 50% of their income to go to those kids (and most don't order that high an amount) it's only $250 per household per month (if each wife had 2 kids). thats less than the minimum basic adequate standard of care that welfare uses to issue grants, so the kids would still be eligible.
it's abuse of the system-but there is a reason your rarely if ever hear of a polygamist being successfully prosecuted for welfare fraud-they know the system inside out and operate withing the letter of the poorly written laws