Can you live and rejoice while in lake of fire? It's taken more than good sun block and thick pair of shades to live there, I think you couldn't live there on based of your flesh and blood.
Well, do the next best thing, if you can't live on the surface of a star. Create a new tech line and live in star's grav well.
You can already build four starbases in a star's grav well, with the new tech line you can build other structures that are hardened to resit the harsh gravity and temperatures being so close to a star.
Imagine defense structures guarding phase lanes to the interior of a system, or some shield generators to protect other objects from a star's fury.