You do not swallow saliva in your sleep because facial muscles are relaxed. Most people wake up with saliva in their mouth, which is instantly swallowed once that person wakes up. While sleeping, people do produce saliva, but it is significantly less than when they are awake.
Drooling, which is the production of excess saliva, usually ensues when a person sleeps on her side. When a person sleeps on her back, drool isn't formed because excess saliva settles at the back of the throat and travels down the throat. Saliva is essential in keeping teeth healthy, fighting germs, staving off bad breath and keeping the mouth moist.