Does the emission of a small layer of saliva or things from the stomach during sleep, and a part of it entering the pharynx after waking up, constitute an error during fasting, nullifying the fast or not?

If the discharge from between the teeth is slight and unavoidable, or was swallowed by mistake, there is no harm and the fast is not invalidated. However, if it is abundant and the person intentionally swallowed it, their fast is invalidated, as the fast is broken by intention, not by forgetfulness.