Theoretically a lot of stuff can happen. As a practical matter, this has to be regulatory. Eggs and chicken meat is a very well understood product and by nature a completely normal market. I've literally been offered chicken meat by roadside sellers who butcher them on the spot and cook up a meal; it is a bit gruesome but not outside the complexity of operation that one family can manage.

The part of the supply chain acting as a "monopoly" is too simple to replace. Someone can literally set up a new local butchery, buy directly from the farmers and the exclusive dealership network is broken. Probably need some know-how and a refrigerated truck. It is barely possible that the sort of monopoly structure being described could have been built over the entirety of the US without regulatory support. It'd require something approaching a mind control ray to keep the competition under control.

I believe the other comment saying that chickens are a bad business, competition would tear through the margins like a rooster eating a mouse. But a country wide monopsony on chicken purchases is absurd (unless the regulators are pushing it). If nothing else there are a bunch of low-income people who'd be happy to buy and butcher their own chickens if it cut out a middle man. It isn't feasible to build a natural monopoly.

Theoretically, it is possible to do anything of that, but what is missing from your business plan is selling a commodity product at scale on a competitive price. And if you somehow manage to do something like that, nothing stops the big player of your region from going to any of your clients and offer them dumping prices for ditching you or going to the local vendors of animal antibiotics and offering them premium price if they supply only chosen farmers thus squeezing you and your suppliers from both ends.

If you have a market with low margin and no differentiation between the offered stock, the gains are in size and it logically leads to a few players in the market so I doubt that the independent butchery has to be butchered and won't die of natural causes due to high costs or because a few of its partners are having a bad year.

The horrible thing is there can be lots of differentiation here. I grow my own meat birds for my own consumption, and they taste radically better than anything I’ve ever had in America. (Barring when I eat my friends’ birds.) Artisanal chicken could definitely be a thing, although it would definitely cost more.

I feel that regulatory capture is part of the problem - processing your own birds is safely is definitely possible, but what is required to process them for sale makes it so the local USDA butcher would have to charge as much for a chicken as for a sheep, and that’s just not viable.

Aren't both of the examples of what they could do illegal ?

You saying that consumers having meet on dumping/low prices is illegal? You are a communist! /s You saying that a businessman is obliged to go against their own interest in stead of selling their meds to the highest bidder? You are a communist! /s Free market without regulation is exactly that - freedom for those who can shape the market as they wish and no government violence necessary so it is kosher.