Yes. They will be subsidized, just like other food-based welfare programs.
As for the rich, is this really your concern? A few rich people getting some cheaper groceries is so bad that we have to deny poor people from getting affordable food? Why do so many Americans hate poor people? You know there's literally trillions of waste in agriculture, military, pharmaceutical, oil, etc... subsidies and that's just the tip of the ice berg if you examine the tax code. If you're deeply concerned about rich people gaming the system, why don't you start in those places and then when we figure that out, we can worry about rich people shopping in one of five total grocery stores.
