Short summary: Tabbys Star is the one that has the mysterious dips in brightness that some have suggested might be because of a Dyson Sphere, but according to the article, that proposal is just as unlikely as anything else that has been suggested (due to the lack of IR-emissions).

To solve the mystery, they need to get observations during a dip which costs them money for the telescope time. Tabby has a Kickstarter campaign to do this, and she's asking for 100k USD. With 4 days left, they still need some more money.

I think I'll donate to this one.

https://www.kickstarter.com/projects/608159144/the-most-myst...

If whatever is stopping the light from reaching us is reflecting the light rather than absorbing it, could that explain the lack of IR?