but it I can't make sense of how the government will give you money to support your family even though you have child support arrearages?
Should they be left to starve while they seek work?

Child support is based on income. If you're not earning income, you're not going to be able to pay - not child support, not your own basic living expenses. It's simple arithmetic.

While I'm certainly sympathetic to your problem, I'm not sure what you think should be done here, as assistance payments cannot be attached.