This is our dog, Tuck. He was found in the ditch when he was about 6 weeks (we're guessing) with his sister (again, we're guessing). His right front paw pad was sliced off and his sister was also injured. We don't believe that this was an 'accident'. The family that took him in were told by the vet that his paw would never heal. We got him a year later as they lived in a small house on a small corner lot in town and he had gotten too big and energetic for their baby.
For at least the next 4 or 5 years, the pad would not grow back then suddenly, and miraculously, last year it did! I have always thought that his leg had something wrong (from when he was a pup, also) but the vet thought not. He looks quite comical when he runs because he favours his right paw. His head really bobs up and down because he is essentially running on just his front left leg. The right is just along for the ride, although it will completely bear his weight. In the top picture, it looks like half of his leg is missing, but it's all there...including the pad! In the other pic., he getting ready for a drink in an area that is very wet. He likes to roll around in the water then wants in the house!