This phenomenon is well known and usually called a "Poverty Trap" or a "Welfare Trap".

http://en.wikipedia.org/wiki/Welfare_trap

One of the things that can mitigate this is the Earned Income Tax Credit (http://en.wikipedia.org/wiki/Earned_income_tax_credit)

Also, it is misleading to claim that "the poor don't work". This article only discusses people below the poverty line ($11,490 for an individual). If you work 1600 hours per year at the federal minimum wage, you earn $12,000. That's definitely poor in my book.