first, this would be voluntary, something people would opt into, if you do not opt in and have one child, you'd be eligible for government assistance via entitlement programs, if you have a second child while on government assistance, you would not be eligible for any government benefits for the second child unless you opt to have a reversible tubal ligation (tubes tied) post delivery.
secondly, this is just a hypothetical, I haven't considered which governing bodies would be responsible for enforcing this sort of program, and it's not exactly important as this is only hypothetical and the idea is only in the planning stages.
as far as your scenario goes, the foreigners wouldn't be criminals at all, they just wouldn't be eligible for government entitlement programs so it really wouldn't matter how much they earned a year, whether they can afford them or not is entirely their problem, they created six children and if they aren't able to afford those children, there's always the option to put some of them up for adoption.
This theoretical program would be created with those in poverty in mind, such a program would offer a reversible vasectomy or tubal ligation and also supplement that with government entitlements, and during the period that these parents aren't able to reproduce, they can spend their time learning new skills or trades, obtaining a higher education or serving in armed forces all while not having to worry about raising children they cannot afford to feed. when the person decides they are ready to bring a child into the world and they've met the criteria to be eligible for a reverse vasectomy or tubal ligation, they would have the procedure and then go onto procreate, the benefit of this is that the child would clearly have to be planned as the only reason to request a reverse procedure would be because that person wants to procreate.
In my opinion, bringing children into the world you can not afford is criminal, the hypothetical above does not suggest these people be imprisoned or criminalized, but if they continue their reckless behavior, birthing children they can't afford, they should not be rewarded with government benefits for their continued recklessness.
do you have a realistic alternative?
. Now this is interesting, because what you feel so strongly (raising children in poverty), your legislation would basically guarantee that both (and all other children born thereafter) would be raised in poverty 
