That never happens with woofers. A square wave is a sine wave plus all of the harmonics of that sine wave all at the same level. That's explained within this post:
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No musical waveform ever has enough harmonic content to be a square wave. It might be close with a fuzzed out guitar or synth, never with bass. Also, woofer voice coils are inductors. When a signal passes through an inductor the highs are filtered. If the inductor has a high enough value all of the harmonics will be filtered, and when that happens what you end up with is: a sine wave. A woofer voice coil doesn't have that much inductance, but it has enough so that the power the coil has to dissipate is no more with a clipped signal than a clean one. Tweeters can be damaged by clipped wave forms, because they are subjected to much more power than normal. That's why guitar amps don't have tweeters. If clipping killed woofers they wouldn't be able to use those either, but they don't.