It's actually like a Zen koan: "Can you blow a speaker by underpowering it?" is almost as deceptive a thought experiment as "If a tree falls in the forest and no one is there to hear it, does it make a sound?"
Both queries force the asker (or the askee) to make a semantic interpretation before an answer can be given.
In the case of amps/speakers, the red herring is the word "underpowering"
Since conventional wisdom (as well as occasional empirical evidence) suggests that you can indeed blow a speaker by putting more than the rated power handling capacity through it (aka "overpowering"), that same line of semantic reasoning figures that if you can also blow a speaker by putting less than the rated power handling capacity through it, that must be called "underpowering" and this underpowering is what blew the speaker.
But that's wrong on both counts:
- The word "underpowering" has no useful meaning in terms of the amp>speaker relationship; it's only a useful word in terms of the sound system's sound pressure level output capacity relative to the room/audience size (presuming one also takes into account speaker sensetivity, dispersion, etc.)
- Secondly, the thing that blew the speaker was in all liklihood amplifier clipping...which may have been caused because you were trying to exceed the sound system's maximum sound pressure level output capacity, but regardless, it wasn't because there was too little power going through the speaker.
You can damage a speaker by "underpowering" the PA system you're using it with in certain circumstances, but you can't damage a speaker by "underpowering" it.
See grasshopper?