If there is no rubbing even when biasing the cone in all 360 degree directions, (displacing slightly its axis), I would suspect something has become detached.
There is also the slight possibility that something is being attracted to the magnet and being pulled against the cone by magnetic force, and rattling when the speaker is used. I have seen this on tweeters, in fact my new ATC 50s had it and I removed steel fragments carefully with a screwdriver with another magnet attached. WITH MUCH CARE.
It may be a few overheated turns of the voice coil, and they could possibly be re-fixed with a little superglue inserted into the detachment 'crack', removing all excess immediately. If the V/C is detaching from the cone araldite is suitable, this being used by ATC to attach V/C s to cones, in their case I believe 'quickset'. If the cone is plastic I would use superglue for this as well, but of course it is not much of a gap filler and better for fine crack breaks.