What would happen to the food chain if there was no rain at all?

Carnivores eat herbivores, but they also eat omnivores, which is another category that combines the herbivore and the carnivore. Certainly there would be much less food available to carnivores if all the herbivores were gone, and the number of carnivores would decrease, but as long as there are still omnivores, then there is the opportunity for some carnivores to continue to exist. For example, we human beings are omnivores, and even if all the herbivores were to disappear, we would find a way to continue to feed our pet dogs and cats, which are carnivores. Pigs are also omnivores, so presumably we would still have them as farm animals and food sources.