Not sure if this is exactly your issue, but speakers in the low/mid range typically use a voice coil actuator – it pushes and pulls air when an electric current or voltage is applied. If that were to exceed a practical input voltage range, the actuator could be damaged by exceeding a physical travel range.
High frequency speakers (tweeters) typically aren’t voice coils but some surface vibration that can operate faster (but not push more air). Not sure if those are “blown out” often. With a nominal range of power input and control voltage/current, they would “filter” out the out-of-range frequencies using an electronic filter (crossover) or just not be able to reproduce them.
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