removing broken mudguard/fender bolt from eyelet
You could try slicing, with a dremel or similar instrument, a 'notch' into the bolt that would allow a flat edge to fit in. 
Soak the bolt/area with a penetrating lubricant (PB Blaster or some such) or ammonia, let it sit and do its work for a few minutes (some folks recommend 24 hrs), and then attempt to 'tighten it through' the eyelet.

You could also try to heat it w/ a propane torch for 30 seconds or so and then try again to tighten the bolt through eyelet.