Why may animals die off there fewer plants around

Animals depend on food and without food it will break our animal food source chain. for example cows depend on hay and lions depend on meat from cows or something like that 

Because plants are producers they hardest the power of the sun witch they convert in to energy and when herbivores eat them they now gain energy needed to survive when carnivors eat them they pass it to them so if there were not enough plants none of the animals would have the energy they need for reproduction so the animal would slowly die off