It's heat that fries voice coils, not a specific waveform.
If the voice coil gets hot enough, something bad will happen (glue melts, metal deforms, voice coil former ignites, magic smoke escapes, atoms split, known universe collapses into a singularity, Chuck Norris loses a fight, whatever). A big enough megazap of power can fry a voice coil virtually intantaneously, or a steady application of more heat than it can dissipate over time will do the same thing.
A high power amp can zap the voice coil, or slow-cook it. A low powered amp's only hope to kill the speaker and get the rest of the night off is the slow-cook. Here's how that can happen:
The more deeply an amp is driven into clipping, the higher the *average* power it's putting to the voice coil is. So if an amp is powerful to put out a distorted waveform whose average power level exceeds the thermal capacity of the speaker, it can theoretically kill the speaker if clipped long enough and hard enough. However, a more powerful amp driven to the same average power level (without clipping) would kill the speaker just as quickly.
Clipping is especially nasty to tweeters because the crossover routes the higher clip-generated harmonics to the tweets... but that's another story for another day.