Can gain to the maximum destroy the speaker?

Answer 1

Yes they then crack and are like Zzzz zzzz zzzz zzzz zzzz 

Answer 2

The short answer is no, however if you use an amplifier that increases the speaker's volume higher than it was designed to go then yes.

Answer 3

If the instantaneous peak is higher than your speaker is rated, it can destroy them.

Answer 4

Yes, it can.      

Never operate anything at maximum.  

Answer 5

If the instantaneous peak is higher than your speaker is rated, it can destroy them.

Answer 6

The correct speaker should be able to cope with the peak output of the amplifier.

Speakers can cope with transient spikes but not prolonged abuse. They don't last for ever. With heavy use, at or beyond their limits, the cone and suspension can eventually suffer reduced mechanical strength, affecting the quality of the sound. A friend purposely caused prolonged guitar and microphone feedback through my speakers. It weakened the mechanical strength so much that the coil began to vibrate against the magnet, making the speakers useless.

Answer 7

Yes. High levels of motion can rip speakers. It's wattage at frequencies that are the issue.

But, there are different meanings for gain. The issue is decibels, volume.  

https://www.musicianonamission.com/gain-vs-volume/