I don't think this is actually possible. It's pretty easy to paint over the bottom of the floor without hitting the cliffs though.
One thing you can do is add the base as a painted texture and just paint it on the cliffs. But doing that usually creates blocks of painted texture as opposed to smooth brush strokes. So you might have to cover it up with other painting on the edges.
You can change the base texture of a terrain though by using the side bar, that won't delete your terrain raising/lowering if that's what you mean.
