This idea evolved into what’s called a Dyson Sphere, a gigantic sphere that completely encloses a star. It was popular back in the 1970s and 80s; there was even an episode of Star Trek: The Next Generation about one. Dyson never really meant that we’d build an actual sphere; just lots of little panels that might mimic one.
But it raises an interesting possibility for detecting alien life. Such a sphere would be dark in visible light but emit a lot of infrared. People have looked for them, but we’ve never seen one (obviously).
Which brings us back to KIC 8462852. What if we caught an advanced alien civilization in the process of building such an artifact? Huge panels (or clusters of them) hundreds of thousands of kilometers across, and oddly-shaped, could produce the dips we see in that star’s light.
Actually I would think it might be something I would like to call a Dyson Screen. So that would be a huge solar panel that floats out in space that the aliens living in this star system use to power an entire planet. Maybe there are gigantic batteries along the back of the screen that massive star ships remove and take down to one of the inhabited planets. I'm thinking the planet is a huge manufactorum like Mars in Warhammer 40K that needs tons of power to function. Or maybe it a massive city miles thick that covers the planet like Coruscant. In any case it would be interesting to turn some radio telescopes toward this star system to see if they can get some radio transmissions from the aliens that might live there.