Stars colliding orbit?

It doesn't get that close. Both stars are orbiting around their barycentre, and that is what the orbit line is drawn around. The main sequence star will effectively roll around inside the orbit line and always be on the opposite side of it to the brown dwarf.
 
Yep, The giveaway here is the eccentricity statistic in the first pic: at 0.0303, it's nearly zero, despite being (apparently) quite off-centre.

You can see the tiny orbit-line circle of the primary star, in gray, inside the star - and it's circular-looking too, so the primary star's orbit around the barycentre will likewise have near-zero eccentricity.

The upshot of all this means that these two stars will always appear like that, in pretty much an identical configuration, no matter when you visit them. The distance between the two stars virtually never changes, just like in the Wikipedia GIF linked to by morph113.
 
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