It’s not even necessarily the same processing plant as where the adult chickens are slaughtered for meat.
While this may be true: I have worked at 4 different chicken processing places (though 3 of them were owned by Foster Farms) and they all handled every part of production from farm to package. Both chicks and adults.
And it sucks being on any part of the line that is dealing with the live animals. It’s one of the reasons I don’t eat a lot of chicken any more. One of my first jobs ever as a teen was cutting the toes off the birds so they wouldn’t be able to scratch each other up if they started fighting.
That has to do with the fact that the entire American chicken industry is exploitative to the people raising the chickens as well as the chickens. Since the factory is both the hatchery and the processing plant, the farmers never even own the chickens. They’re more like babysitting them by taking out a loan from the bank. They get squeezed, default, and somebody else comes along to keep it up. Reasonably this sort of business practice should be outlawed as anti-competitive.