Are you saying that the part of the coil which failed is a separate wire from the actual voice coil or in some way 'free floating'? In most speakers - of the single rear suspension type, the v/c is wound on the former with the ends coming up the cone on the inside then soldered to the pigtails where they pass through the cone. The tails of the v/c and soldered joints are glued to the cone inside and the pigtails glued on the outside. All this is usually covered on the inside by the dust dome. There should be little fatigue of the v/c wire anywhere as it should be secured to the v/c former or cone. The pigtails and often silvered and do fail either through gross overexcursion or fatigue leading to overheating. I`ve seen pigtails melted where the voice coil is intact.
You can sometimes rescue a speaker from this condition with some new pigtails and a dust dome. At one time you could buy pigtail wire from Goodmans, you probably still can from Wembley Loudspeakers if you ask nicely.
A speaker which has been seriously overdriven often shows no voice coil damage other than an obvious open circuit in the 'straight' part of the v/c winding. Chances are, your customer was pushing the amps well into clipping and simply overcooked the voicecoils which melted at the weakest point.
Wembley Loudspeakers will repair the drivers at a reasonable cost no doubt.
Ron