The sharp crack you hear on some subs when the bottom out is the voice coil former (bobbin) hitting the back of the magnet!
This can warp the former causing the voice coil to rub in the magnetic gap. The cure for this is a new voice coil, a delicate and in most cases, uneconomical procedure on most home and car audio woofers. Some professional units have field replaceable cones or baskets.
If its hard enough, one bottom can destroy a woofer. A few small subwoofers met their doom this way after I fixed a 200W amp that was given to me when I was 17.... my first taste of real power. (fond memories.... that system lives on now that I'm in college, its just gotten smarter and a lot cleaner but its still the envy of more than a few frat houses)
Some woofers have a "bumped back" magnet which reduces the likelihood of hard bottoming. Soft bottoming is extending the suspension (the spider and surround) to their maximum limits. Over time this can damage the suspension. Once the suspension becomes excessively compliant, the likelihood of bottoming increases.