It's not only possible, it is demographically inevitable and foreordained.
Start by defining "in poverty" as any household below a certain line on the income bell curve. Right there, you have insured that there will always be a mathematically predictable group in the defined class. Now predict the likely occupants of that income bracket: the poorly educated, the dysfunctional, the recently unemployed, large multi generational households, and the young entry-level. Then predict who will be the most likely group to have children: the young adults and the multigenerationals (teen kids having kids, supported by grandfolks).
Bingo, bango: Lots of kids below the poverty line. Doesn't mean their family will stay there, but it's more likely if they have no education and/or are dysfunctional due to lifestyle. Mostly, as the income earners age and advance in their careers, the children rise out of the poverty bracket and are replaced by a new batch.