If SJS acquire Karlsson, I could see Ottawa taking Braun as part of the package. The only top 4 defenders the Sens would have at that point would be Ceci and Chabot. So adding Braun would make sense.
For the Sens, it'd work out well since Braun has two years left. He could probably be flipped in 2019-20 for some futures after players like Jarod and Wolanin hopefully establish themselves as NHLers.
With that said, I am talking from a perspective of if EK went to SJS, and not necessarily endorsing that as something I'd want to see personally.