Also FWIW "deep" and "mild" filters =
no such thing in any objective sense. There may be a specific filter effect with a "deep" or "mild" switch on it, but that is just a convenience of labeling on that one unit. Also, a filter can be any adjustment of the frequency response/range- so the way it's stated above would imply that rolling back the tone knob on your bass is a "speaker killer" for example, or adjusting the EQ on your amp.
If you're talking about a resonant filter, especially one that sweeps through a range (like an envelope filter or auto wah) then yes the resonant peak of that filter
can be a speaker killer
if the resonance is strong enough to cause a voltage swing many times higher than your normal signal.
Yes, there are some speakers that are more resistant to that kind of damage, but the safer, smarter approach is to use a limiter to rein in those big resonant peaks.
Again though, as bm1185 said, the idea that certain waveforms "kill speakers" is a myth. Though technically a square wave at high amplitude can damage a tweeter if the tweeter has too low of a power-handling rating. I can explain that in more detail if you like, but also be aware that this subject has been covered very, very, very thoroughly over in the amps forum.
