I'm not an astronomer, so I don't know if something like this would really be possible, but how about a cloud of dust that was so slowly drifting towards the star that it was caught by the star?
The cloud of dust would, so to speak, wrap around the star.
This could explain the more than 100 year decrease in the brightness of 'KIC 8462852' because more and more dust is accumulating around the star.
The stronger fluctuations in brightness would be explained by denser dust fields within the cloud. Likewise, the more or less regular fluctuations.