This hypothetical scenario has no basis in reality, at least in the US. Besides the fact that children in the US have access to free meals on a daily basis through public schools, food in the US is dirt cheap. Food deserts basically no longer exist in the US thanks to stores like Walmart. You can easily supply a nutrient-filled 2500 kcal diet for under $3/day in the US. For most people who are desperately poor and unable to do this, it is an educational problem; a lot of people just don’t know how to eat healthily.
Please don’t make shit up off the top of your head.