This (Tabetha Boyajian) abstract suggests, if I read it rightly, that something in the past broke up the star, leaving a whole lot of obscuring stuff floating around it.
“Over the duration of the Kepler mission, KIC 8462852 was observed to undergo irregularly shaped, aperiodic dips in flux down to below the 20% level. The dipping activity can last for between 5 and 80 days. We characterize the object with high-resolution spectroscopy, spectral energy distribution fitting, and Fourier analyses of the Kepler light curve. We determine that KIC 8462852 is a main-sequence F3 V/IV star, with a rotation period ~0.88 d, that exhibits no significant IR excess. In this paper, we describe various scenarios to explain the mysterious events in the Kepler light curve, most of which have problems explaining the data in hand. By considering the observational constraints on dust clumps orbiting a normal main-sequence star, we conclude that the scenario most consistent with the data is the passage of a family of exocomet fragments, all of which are associated with a single previous breakup event. We discuss the necessity of future observations to help interpret the system.”
As Bradley Schaefer writes describing what this would mean in terms of a bunch of comet-like debris:
“the century-long dimming trend requires an estimated 648,000 giant comets (each with 200 km diameter) all orchestrated to pass in front of the star within the last century.”
So an astronomical crapton of crap, arranged to block light between that star and us, with darkens by the same 20% on some days, and then has also dimmed the star’s light by 20% over a span of 100 years, which seems improbable… to Schaefer, as our system has one such comet (Hale Bopp) which is less than half the size of what’s calculated to be needed in the model with 648,000 such objects.
I haven’t heard a theory that seems more likely, though. I’m no astronomer, but I wonder if it’s not that either the star or planets in its system experienced some major collision in the past, leaving a lot of dust in the system, and the pattern we are seeing in dimming is just the pattern that the dust is arranged in the system as it drifts about that system… like there are some bands, and well as a general un-evenness that has been getting denser between us over the last 100 years.
As for Starkiller Base, I would suggest that KIC 8462852 may be a metaphor for logic in Earth fiction, though then I would expect a sharp drop around the release date for Episode VII.