Build Your Own Subwoofer
My take on that was that there is no *internal* crossover. A real subwoofer should have an active crossover before the (dedicated) amp. This pretty much goes for any situation - The one exception may be (but usually isn't) the LFE channel on surround recordings, where the channel only contains low frequency sounds. Most surround preamp/receivers do low-pass filter this channel anyway before sending the signal out, and many active subs have a built in adjustable active crossover (before the included amp, so one could argue that it isn't part of the subwoofer).
Anyway, a proper system design would ensure that your sub would never receive 10KHz tones, and therefore you would be safe from the cone breakup effects, etc..