With less predators to eat them, the rabbit population will likely go up if the fox population decreases; assuming there are favorable factors such as plenty of food and habitat for the rabbits. At some point, there is a maximum limit to the number of rabbits that a certain location can hold. Once this limit is reached, (some of) the rabbits will migrate elsewhere or unfortunately die off.
As the rabbit population increases, the fox population may rebound and start increasing again. This is due to more food being available to the smaller amount of foxes, and there is less competition for food. So the rebounding fox population will likely bring down the rabbit population to a point where food will get more scarce for the foxes. This cycle repeats itself where one population increases while the other decreases, and vice versa. They are very strongly linked together. It's also possible that both will increase together if environmental factors are favorable, but they could easily decrease together if a habitat is being destroyed for instance. It will depend on the circumstance.
