On the contrary, YOU are making a terrible assumption there. Why on earth do you think people would let them go extinct? Most people who don't eat animals do that because they LOVE animals. So why would people who love animals enough to not eat them let them go extinct? That makes no sense.
As it is now, there are farm animals who were rescued from the meat and dairy industries and are living their lives out in animal sanctuaries. As time goes on, I think there will be more and more animal sanctuaries, because there are a lot of people who love animals, and believe that they have just as much right to live on this earth as you and I do. To think otherwise is arrogant, anthropocentric and cruel, in my view.
Speaking of animals being rescued from the meat industry, here's a fantastic story. I hope you take a few minutes and check it out.