Lordsummit mentions plastics. When you submit a plastic sample to something like an Instron tensile tester (it gradually pulls the sample apart), you can stretch the material just so far until its elastic limit is reached - beyond that, it is permanently deformed and won't return to its original shape. There then follows a period of non-elastic deformation until break. In this form, it is more brittle.

The elastic limit of copper is very low (it doesn't take much of a bend to be permanent), but perhaps in the area between permanent deformation and break there is a similar decrease in elasticity that allows it to break.

However, to return to the point of departure, I can't see anyone accidentally torturing their beloved cable to such an extent that the sound changes!