I'm not sure what's wrong but I've had something similar happen to me when I was out shooting a few years ago. The shutter plate wore out.
However, when this happened it stopped taking photos in the middle of a burst of photos. The second to last frame was normal but the last frame had this large out-of-focus black line through it (Like yours). Then it wouldn't take any more photos but I think it still turned on. Anyway, I had to get it replaced. [size=78%]This might be the problem but I am not very knowledgeable with camera repair.[/size]
Is the camera still under warranty? The shutter count on a Rebel T6i is supposed to be good for about 100,000 shutter actuations (According to a quick google search). If your shutter count is significantly less you may be able to convince them to replace it (It took me quite a bit of arguing but eventually they agreed to cover the cost. I think my shutter count was about 30,000 at the time.)
If it is not under warranty, you would have to send it in for repair. I think when it happened to me, they originally told me the cost would be about $350 (This was for a Nikon body and through Henry's though).
Once again, I'm not sure if this is the problem.
Good luck with fixing it.