I have a different answer than Greg has. I think this saying refers to the fact that dogs chase cars, and they act very "tough" when they chase them, but they never actually catch cars. What would a dog do if it actually caught a car? Answer: It wouldn't know what to do. The dog would be unable to hurt or defeat the car, so all of the chasing turns out to be pointless. So, the idea of a "dog who caught the car" refers to a person who is pursuing some goal that he/she cannot enjoy or take advantage of, even if the goal is achieved.

"What is a positon 'of the dog who caught the car'?" It means the dog was hit by the car. Example 1: "My dog was always chasing cars. It finally caught one." (it finally got hit by a car) Example 2: "That dog down the road finally caught a car." (the dog was always chasing cars and it finally got hit) You have to be very careful on usage as it is injecting a somewhat dark humour onto a not very positive thing.