As Bill stated they probably made the last batch of chicken at a predetermined time. Like pretty much all businesses they rather not pay overtime. They sell what they have left. And start shutting down equipment to get out at probably 10:30. I've been to other churches locations and I guess it all depends on the amount of local business they have.
Just a guess but Church's makes small batches of chicken at a time. If they didn't close there door early and it was busy they may not have what you want and if they had to make more they would be there all night. You've never been locked inside a closing store before I gather.
Sometimes staff in a store will only continue serving customers already inside their store before actual closing time. Even when putting this practice to work, they could still end up with customers inside after closing. Letting me customers entered in the last ten minutes guarantees they will not be served before closing time. B
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