How can an increase in biodiversity lead to an increase in ecosystem stability?

Here's an example to help explain; biodiversity is a the amount of species in a specific area the larger the number the more likely more will survive should one of these be killed off
say we have a system w/ grass bunnies and wolves not very diverse  so bunnies eat grass reproduce and are eaten by the wolves however say the bunnies die off somehow the wolves will then die because they no longer have an accessible source of prey because they don't eat grass 
now lets say that along with those three creatures there was also small rodents as well a large population of deer and other animals now when the rabbits die off the wolves have a separate food option allowing them to continue to survive until their original preferred comes back or they are forced to adapt to hunt their new prey
essentially with a larger biodiversity when one key animal dies it doesnt turn into a snowball effect because there are other animals that can fullfill the missing animals place in the food chain

True. you know, tools like shovels.