What frequencies blow out the speaker most?
Speaker damage (not destruction) is very often caused by heat. The gap between the moving voice coil and the fixed magnet assembly is very small. Any distortion of the cylindrical voice coil can cause rubbing. The effect is audible, but the speaker still "works". Carefully pushing the cone (with even pressure) of a disconnected speaker, you can hear  or feel the scraping sound. That's a damaged speaker.
Heat can also cause the voice-coil windings to de-laminate from the cylindrical cone they're wound on. Again, you can suffer scraping in the small gap. Of course, enough heat breaks the wire, and the speaker goes from a few ohms to infinite ohms.
Some of those low-frequency speakers can bottom-out, where some part of the voice coil smashes against the fixed magnet assembly. The voice-coil cap may pop off, the attachment point between cone and voice coil may rip, or the voice coil distorts and, as above, scrapes in the gap. The spider (the corrugated mesh that keeps the voice coil centered) might also come adrift. These damages are usually audible, but the speaker still produces sound. Not a usual failure mode for tweeters. Can be caused by an unexpected loud blast or turn-on transient. This one can happen without the usual heat-related damage.
Another failure mode not heat-related is failure of the flexible surround that attaches the cone to the basket. These are made of light materials, and take a lot of flexing, especially in bass speakers. Heat, sunlight, chemical decomposition can stiffen the surround material causing cracking, or detach at the glue joint.