My two cents worth.
This game is something of a WWII historical endeavor so consider this as a possible basis to settle this issue.
WWII gun camera footage primarily determined kills awarded, i.e. generally, if the plane is seen to be destroyed, a kill is awarded, if not, no kill. In other words, even if a pilot shot the heck out of a plane, but it flew off into the sunset, no kill. Moments later, another pilot comes along and slaps the final round into it and it goes down. Seen in his gun camera, a kill!
No matter how many rounds you put into a bandit, no matter how much damage you inflicted, if it doesn't go down, you didn't make a kill. Period.
Therefore, if another comes along and pilot puts one round into that damaged plane (given it could conceivably be landed and repaired thereby not requiring a replace aircraft be manufactured), then he finished the job that YOU failed to complete. You get an assist, but he actually destroyed the enemy aircraft (with your previous assistance) and should, therefore, receive the kill.