Absolutely right! Always carry a pair of prusik loops. Practice with them. Practice improvising one from the end of the rappel rope. Read Touching the Void and practice some more.

By the way, should your descender become jammed, DON'T USE A KNIFE TO CEAR IT!

Nylon under tension cuts VERY easily. The fibers practically split at the mere sight of a knife blade.

Both the posts above are good and accurate. It is really a good idea to tie a knot in the end of a free-hanging rappel rope, or to tie in the bottom end of the rope to a fixed anchor. I would have lost my life many years ago in a climbing accident on El Capitan (at night) ... but for the fact that my partner was smart and fixed the bottom end of the rope to a bolt anchor on the cliff face.

Prusik's - or better still ascenders - are really essential gear also. For any kind of complicated rappelling they are absolutely essential.

I'm not sure any of these precautions would work with 1-inch webbing. That's one reason why I want to try it out.

Pete