Suppose a supermarket stocks chickens in units of 1,000. If you buy two or three chickens every month, and then stop, you probably won't cause them to stock 1,000 less. But you might if the supermarket is just at the threshold between order sizes. That will likely only happen about 1 in 1,000 times you buy chicken — but when you do, you save 1,000 chickens.That's right, you will save a thousand chickens. The farm will just continue to feed them, and they'll live out their lives in poultry bliss because of your virtuous decision not to buy a chicken.
No, they won't. If they can't sell them to the grocery store, they'll sell them to the rendering plant. If you don't eat them, your dog will eat them in his dog food, or they'll be used to make glue.
What may happen if enough people stop eating chicken is that fewer chickens will ever be born. It would be very odd to describe this as "saving" a chicken: there will never have been a chicken to save.
If you want to reform factory agriculture, fine. I like farm fresh eggs that come from free range chickens, and that's mostly what we eat -- a friend of the wife's has a whole bunch of them. I agree that, in general, we should try to structure our relationship with animals in a way that is humane and respects the animal's nature.
But come on. Before you set out to reform an industry, at least learn how it works.