Definitely broken, I've seen this on Ducatis before and its a sure sign to me that the chain has snapped on this bike at some stage in the past, it will have bunched around the sprocket breaking the metal at the front and will have whipped up breaking it directly above the sprocket. On an air cooled Ducati like mine that would have burst the crankcase but fortunately it seems less terminal here. You can get strips of steel that bolt on as protection on the Ducatis but they have convenient bolt holes in that location to attach it to.
The next day I did have a good look at the bit I initially thought had just been caught up in the chain run, it was fibreglass matting, probably stuffed in there as a bodge it type of temprorary fix.
I may try and rebuild the broken part in front of the sprocket with chemical metal,or possibly attach an extension to the steel separator plate in the cover to keep the muck and chain fling out of the gap where the flywheel/generator lives, probably the same reason the a previous owner put the fibre there, only mine will be more secure and held in with more than gunk. It wont protect against another chain break but it should keep the grime confined to the sprocket well.
Interesting evidence of the bikes history though.