What would happen to an ecosystem whose number of predators declined due to over hunting and disease?

The prey of that animal would increase in population and then end up killing itself over thousands of years by eating all of its sources of food, due to overpopulation.

Explanation:

Without predators to keep the other animals in check, the second-on-the-food chain animal would overrun the area and, due to so many of that animal's kind to feed, it would end up eating all of its food and eventually kill itself.