Simple,
you have the predator/prey relationship, simple.
BUT, if rabbits were wiped out, then how would the coyotes survive?
Unless they find another source of food, or go vegetarian, they will most likely die out due to the loss of their food.
But, if some of the rabbits WERE to survive, than it would be survival of the fittest; the biggest and baddest coyotes would be fighting over prey, and only the strongest will survive in these types of conditions.