The ecosystem of a certain area exists and survives in a state of dynamic equilibrium, where each species in the food web can only grow in population upto a point defined by the "food" available in the ecosystem. Therefore, "food" is the limiting factor which determines how many are able to survive.
It is a given that the bigger the biodiversity (number of species), the "healthier, i.e. steadier" is the ecosystem. Consider how many different options on food each individual gets... Should overpopulation occur (the reason why is another matter), the demand for food will increase,so food availability will be limited, not only for the overpopulated species, but also for other species who are fed by the same source of food. We know that within food webs the flow of energy via food is the crucial factor that determines the survival and thriving of all involved species. One can understand that not sufficient food will mean extermination of a number of (starving) individuals, who used to be themselves prey for other animals and so forth. This process will cause a temporary imbalance in the food chain. Species that are too vulnerable may disappear leaving room for the rest of their competitors. This means reduction in biodiversity,so there will be fewer food options for the rest, which is actually bad for the ecosystem as a whole.