An AC voltage signal with the peaks "clipped" off are sending DC voltage to the coil. At frequencies near the stall mode of the driver where the movement is such that it cannot force enough air over the coil relative to the input power, AC is dangerous enough, let alone DC from clipped output. If the power being applied is below the thermal rating of the coil but very near it, sending DC to the coil from very low frequency waveforms that are clipped for an extended amount of time will indeed cause the coil to reach it's thermal limits. You can have driver failure due to clipping.
Clipping is one of the reasons some people end up baking the tweeter so easily. When the waveform going to the tweeter is severely clipped and harmonics begin to reach the the maximum output potential of the amplifier, it begins to resemble a square wave. Or if you will, AC with portions of DC. The tweeter's coil cannot dissipate the heat being generated by the DC voltage from clipped input, not only because the mass of the coil is tiny but also because it's not moving or forcing air over it to cool it. Thus the implementation of Ferrofluid.
It's worth mentioning that complex musical waveforms blending together can also cause DC current to be applied to the coil while operating well within the unclipped power range of the amplifier. DC is the killer.