Borzoi owners warned me that these dogs can be prone to kill small dogs and farm animals, tend to run too far and for too long and get lost and, because they run so fast, they can hit fences, trees and other objects and break their legs. Even when running on a fresh plaughed filed, they can hurt their legs.
We got a pair of skid boots for him because I was tired of skin tears on his ankles, but any sighthound has that problem.
If I take Strider out to run in a huge area (like my aunt's 20 acres pasture, or capital peak where the snow pictures were taken) he stays fairly close and if there is another dog he pretty much packs up with that dog and stays with that one. With our terrain, if he tries to course an animal he either catches it right away, or it gets up a tree before he can get very far away.
I think his most impressive catch was a swallow in an open field.