Bone is a phenomenally plastic and responsive tissue. An injury such as a fracture immediately sets in motion the series of events needed to restore normal architecture; the ability of the various cells involved to take on whatever role is needed have a great deal to do with the rapidity of the response. The reserve fibroblast in the periosteum almost immediately begin to undergo re-differentiation first into chondroblasts, later into osteoblasts, making the temporary scaffolding of cartilage to bridge the break, and later the woven and lamellar bone to heal it. Repairing a break is essentially the same process as making bone de novo in embryonic life, with both endochondral and intramembranous events occurring simultaneously.
The younger the animal the faster this happens: there's a saying in emergency rooms that if a child breaks a bone, "...so long as the two ends are in the same room, they'll knit." Older individuals have a slower response but even they have enough reserve bone-building capacity to repair just about any break. Fixation of the fracture by some means is needed to hold the pieces into the proper relationship, because if they aren't fixed...they're going to knit together anyway, and failure to keep them aligned will result in a deformity and probably loss of function.
The image shown here is a beautiful example of what bone does in response to injury. These are humeri from a white-tailed doe whose skeleton was found in the woods. One humerus is perfectly normal: the other, however, was at some time hit with a shotgun load of small birdshot, one of which can still be seen embedded in the bone (arrow). The injured leg was completely shattered into a mass of small pieces by the impact, and the fragments have formed a large knobby "repair" that's left this bone several inches shorter than the normal one. Now, this is a very old injury. The deer was mature (note the lack of distal and proximal growth plates) and it would have taken at least a year—probably longer—for the "repair" to reach this fully formed state. Obviously this doe would have had no use of that leg throughout her post injury lifetime.
Fractures from being hit by a car are almost always avoidable. They're usually the result of the owners' unwillingness to use the two things that prolong a dog's life more than any therapy or veterinary-approved dog food: a leash and a fenced yard.