I have done this and it is quite interesting, and the soap actually feels really good after it is done. i would not want the yucky brown liquid, from the salting, out on my teeth either!!
This is from Zany in the soaps- n- lotions forum: I don't have any notes from when I tried this technique, but I do remember it was fun and pretty easy to do. Just trust your own judgment and go for it. Takes all of about 15 minutes.
Grate an 8 oz. bar of soap. Add it to a pot of "Sea Water" (1 oz. sea salt in 32 oz. water) at a rolling boil. The result is almost instantaneous. The soap curdles and the curds rise to the top, leaving a brown gunky water on the bottom of the pan.
Skim the curds off or pour through a strainer and let it "drip dry". Once it was cool enough to handle, I put it in a nylon hose and hung it on a banana holder near the kitchen sink (real technical, I know -- use your imagination to come up with something similar). I formed the soap into a ball and squeezed and shaped it daily to get all the water out. It is difficult to shape at first as the curds don't want to stick, but they do hold together once it dries out a bit. Once all the water is out, take it out of the hose and set it out to cure.
The end result was a hard ball of so-called "pure" soap... the nicest soap I've ever made. But then, I'm in Denver and our dry climate is not kind to skin... I was happy to pour the brown water with the glycerin and whatever other impurities in there, right down the drain. Glycerin draws moisture from the air to the skin. If there is no moisture in the air, it draws it from the skin. YIKES!
I did 3 batches and made 3 balls. The last batch was an OO castile bar and it took the longest to dry and cure. Oh, and one other thing... you lose about a third of the soap you start with.
Hopefully Cee won't strangle me for copying her post...