After destroying the required number of stations, a large ship appeared and destroyed my vessel. Upon respawning, the objective marker for the target had moved approximately 70,000 km to the south west, several whole star systems away. I went back to the area where I died previously and confirmed that my target is nowhere in the area, and the objective marker is likely correct. Somehow the mission to kill greg/ budd (which seem to actually be the same mission, as the station kills count simultaneously and the location is the same) ends with the target ship teleporting far away. I'm now chasing down that objective marker to see if the target is indeed there.