In nature there is no predator whose killings lead to the extinction of the prey. Because then the predator would also be threatened by extinction.

So feral cats- and Donna is right: feral cats are domestic cats -they are not an extra species- are not the reason why birds are threatened by extinction. The main reason are humans: they seal more and more territorries by concrete and asphalte. They have been killing bigger predators for sports- so everything is out of balance.

The answer for feral cats is known and many people at PT do it: TNR!

And of course it may happen that a coyote kills a cat- this is the way of nature.