Like you pointed out, there are a lot of places that simply sell until they're out of food. It doesn't even have to be a place like Franklin's, but many of the really good BBQ places all over the country operate the same way. That's just the nature of BBQ since it isn't something that can just be cooked to order.
What good places do if there are leftovers is to find ways to re-purpose the meat. Obviously, you don't want to serve two day old brisket slices and try to pass it off as fresh to the customer, but you can take that meat and add it to beans, make chili, tacos, add some gravy and make an open faced sandwich, etc.
Still, you want to plan out quantities as close as possible to minimize waste and keep costs down, but a few extra briskets here and a few extra butts there can and will happen. But by being creative and putting the leftovers to use in other dishes or running a special the next day helps keep true waste down to a minimum.