The voice coil has a very small area to work in and if it gets off center it will sometimes rub. This can be caused by uneven torque on the mounting screws causing the frame to warp or sometimes the cone is just out of shape from age,etc. It sounds like a fuzz mixed in with the note and usually ends up with a fried voice coil. If you place all five of your fingers evenly around the dust cover(not on the dust cover) and gently push inward you can usually hear or feel it. If you have a speaker like this try loosening the mounting screws or nuts and torque them evenly to see if it cures it. I have actually gone as far as uneven torque to try and reshape the frame.
Thanks very heplful replies and diagram. Just one more question...other the mentioned cures such as a retorque is a recone the ultimate "fix" or can something else be done? In other words if such a speaker is sent to a repair facility chances are it will be reconed?
Inside or outside of the coil and could be both, the gap is very small. That's why you can over tighten the screws and cause a scrub, the gap is small and the voice coil/former is centered in the gap. If the frame is bent, or the cone gets flexed or wet it could be enough to throw it off center and rub.