Fasting, has actually been proven to be one of the BEST things for the liver!
I never did a salt-water cleanse on any of my past fasts, but I did have a BM in the middle of two of them. (The bowels naturally shut down during the fasting state, so it's wise to have empty bowels when you start any fast!)
I did the salt-water cleanse four times during this fast, because I felt a lot of "gut-work" being done. I felt that it helped me.