That doesn't sound right for a crossover can you post the model of your receiver (I'm guessing pioneer since you said elite).
The crossover actually depends on the speakers the subwoofer is playing with. The BP7006's are actually rated down to 17Hz (but no mention about how many db down that is) so you could actually cross much lower than 80 if you really wanted to, but 40-80 should do it. It really depends on your own bass preferences and I'd advise to play around with it once you get your new sub.
Good subwoofers, such as the ones mentioned, can actually play up to 120Hz and even a bit beyond comfortably. Also, playing frequencies above what a subwoofer is for won't damage it, it just won't play anything.
The what goes to to the subwoofer and the speakers is determined by your crossover or the high pass and low pass filters. You always want to have the filters overlap so there is a seamless transition between your speakers and the subwoofer, but setting the crossover on your receiver does this for you.
Don't think of the crossover as a hard cutoff, it's more like a range +- around the number you set it for.