Sorry to hear about that situation, Nadaka. Welfare traps are nasty, and is why I pretty much explicitly support an actual base income approach rather than a welfare approach. My own family never had things that bed for basic living conditions, but we're all to aware of the way things work - both my parents had to quite their jobs in order for them to be able to afford my brothers medical care - if they worked, their government assistance wouldn't cover the whole thing, and there was no way they could pay the bits it didn't cover with the little they'd make. Thank the gods I've never really been hungry - even when I was homeless I was well fed - but that's not hard when you've got no bills and a small but steady income, and you've only got to feed yourself. And with the medical bills, we either had nothing and my brother died or we had more than enough to keep us comfortable, no real inbetween.
I suppose I can see your point about parents abusing a cash system be not buying for for their children... but I've got to be honest, the families I've seen that would do that usually don't buy food for their children anyways, they'd simply sell the food stamps at less than their value or something to that extent. I tend to think the governments role there is to relocate those children when possible.
Of course, having been involved with the foster care system for a while, I know that isn't really terribly easy either. :/
There are no easy answers.