So bite work would teach a dog to breath with it's mouth closed?

You see back in P.R. I had a bitch (she was the family pet) and all I gave her was bite work. I had a wheel barrel tire hanging from a tree from which she would hang. Now when ever I played with her she would not let go of the rag, she would release only to get a better hold of it, any way I can remember that as she would get tired she would be huffing and puffing with her mouth closed and wouldn't let go. Would this be the result of her bite work with the wheel barrel tire?