I can't remember the title or the author, but I remember reading a story based on a similar premise years ago - the first interstellar ship goes out from Earth to a nearby star, only to barely escape as it goes nova shortly after they arrive. They first think it's just a coincidence, but later suspect that their ship's drive might have been the cause. On their way back home they make up a desperate plan to drop out of FTL drive way out of the solar system to make sure Earth's sun would be safe. This would stretch their supplies, etc. because the flight will now take years instead of months. While traveling they realize that turning on the drive might have had the same effect as turning it off. They stop at the right distance from Earth to catch the light from the time of their departure and observe as the sun goes nova.