In general there is no such thing as underpowering a speaker. You can however, damage a speaker (tweeters mostly, very little chance of damaging a 10" driver) from clipping the amp. Know how when you turn a stereo (or your bass amp) all the way up and it sounds distorted? That distortion is the amplifier "clipping". In short, you are trying to make the amp produce more power than it can and the output becomes distorted. Technically, the waveform is clipped, and that's why it's called "clipping." That clipped waveform can hurt tweeters. Highly unlikely to hurt 10's or larger.
So in short, unless you play your 250watt amp wide open for about a week straight, there's pretty much no chance you will hurt your new cab. Hope this helps.
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The important thing to consider is that a clipped waveform can contain more power than your "rated" output, more like 2.5x, and a lot of this power is in high frequencies. So there's a danger to tweeters any time you start letting your rig distort, no matter what the ratings. But in reality, you'll notice the distortion long before you get to this power, and you don't have tweeters. The risk is exactly the same with a perfectly matched setup--if the stage volume is too loud for you to hear yourself, you can't hear the distortion either, and now you've blown your tweeter. From this, we learn that you should never "right-power" your rig either. You should have both a speaker and amp that are way too massive for your current gig.
Also, if your amp has a built in limiter that works properly and is turned on, it is nearly impossible to blow speakers from underpowering them, because the output will not clip. Of course, you can always generate a lot of distortion intentionally to overpower them, but that's difficult. And some amps are just plain defective (my Ampeg).
I regularly run 300W solid state into my cab rated at 800W. Sometimes biamped with a second cab rated around 700. It works fine, and I'm not pushing the speakers to their max excursion, so it sounds clean. (Of course, if you *want* that max-excursion sound, you have a whole different problem...)
