My experience with the welfare system has been thus: It all depends on who you talk to when you go down to the DHHS office. I've been told during three separate visits that I did, did not, and partially qualified for food stamps...and this is all with the same income and household expenses listed. I've had my household expenses go up, and upon reporting this sudden loss of income had my food benefits go down when they should have done the opposite.
Based on the calculator on their website, I should be getting close to $200/month for food...in reality, I get about $45, which (while I'm grateful I get even that) does not make up for the majority of my paycheck being eaten up by bills. After paying for gas to get to work, and buying food with whatever is left, at the end of the month I'm not only financially tapped out, but I'm eating into the change in my "savings can" to pay for what my income/financial assistance doesn't cover. And keep in mind, I don't have an extravagant lifestyle...this is paying for basic necessities like cheap, non-namebrand food and just enough gas to get to work.
Even with financial help, I'm not even able to basically keep afloat, because I fall into that gap where I technically make too much to get assistance, but my bills eat up so much of my income that I can't afford to live without aid. Unfortunately, the DHHS does not factor in bills when it makes its aid calculations, so it doesn't matter if you (as a random example) make $800/month gross (and around $695 net) but your bills are $950...all they care about is that you make $800 gross and they outright ignore the rest. They're seemingly okay with letting you starve, as long as you have a roof over your head.
As for other types of aid, I've seen SSI and various veterans aid groups completely ignore or discount the realities of people that were too messed up to work by anyone's standards. I've seen people who can't functionally move or who spend the majority of their day screaming obscenities at the wall in a fit of rage get turned down because apparently they're ruled "fit to work" under the logic that somewhere there exists a type of work they could actually do. It doesn't matter that they don't have the skills for whatever work that apparently is, or that (even if they did) that type of work isn't available where they live...all it matters to SSI is that somewhere exists a place they could theoretically make a paycheck, and thus...no help for them. And meanwhile, they're starving. Or they kill themselves, or others.
I've also seen SSI and the unemployment office simultaneously declare someone "fit" or "unfit" to work based solely on whether or not that status would require the agency in question to aid the applicant. And no, presenting evidence of another agency declaring you unfit makes no difference to any other agency out there. I've seen them deny aid to veterans on the basis of the veteran "not having proof that they suffered an injury in the field", when said veteran has documented evidence and records provided by the fucking US Military that says otherwise. I've seen those agencies fuck around deciding the case of a 100% disabled individual for thirteen fucking years before they finally caved, and they only did so because they were threatened with legal action.
So no, it's not easy to game the system. It's damned hard to even get a pittance when you're in desperate need and with legitimate, immediate need of assistance. I talked a bit about how what you get is often determined by who you talk to, but really...for the few people out there who somehow manage to game the system? I have no idea how they do it, aside from luck.