We hear the term "Pure" alot all over the place. It's a phrase coming from horses. I'm wondering has anyone breed a particular "pure" trait a few generations down past it's "pure" parents and kept it "pure"?

Basically what I'm asking is. I remember reading some where about discovering this rare "vien" in the meeroos genetics. Like a koi and that you have to breed that out and strengthen it and strengthen it.

Has anyone tried strengthing a trait/coat/whatever down several generations to see if it's possible to make any of them so strong that no matter what you breed it with the trait/coat/whatever will pass?