As to break in I was thinking more along the lines of the actual diaphragm structure but this would tend to depend on its construction. ie soft or hard, density and construction and in the case of cones whether they are blended with carbon/paper/fibreglass and other compounds.
In the case of a cone, there are several key properties, stiffness and self damping, profile and the termination but this also applies the mid and HF devices.
As such some cone / diaphrapm may give a bit after initial use and so may the termination, possibly those that are semi rigid and designed to operate in break up mode more so than those that are the lossy damped variety.
Odd that many Hi End manufacturers suggest 100 hours playing to break in their systems.