It's unlikely the world would decide all at once to not need farm animals anymore so I think it would be a case of the population falling over years as less were bred.

Also, some species have been altered through selective breeding so much they would have trouble survinging normally e.g. rapidly growing animals that would have difficulty supporting their own weight after the age they would normally be slaughtered.

There would hopefully be more land for wild cows, chickens, pigs etc. to thrive after too.