drooling of saliva is called sailorrhea.
you can do the following to avoid such things-
1. sleep on your back, side sleepers are more prone to this.
2. most if the times, the sinuses can be clogged therefore mouth breathing becomes necessary. because of mouth breathing, your mouth remains open causing sailorrhea. therefore apply some Vicks vaporub or some other balm so that your nose remains open.
3. take hot water bath before sleep so that the steam would clense your sinuses.
4. use pillows so that your head is at a higher level. that will allow easy passage of saliva easily.
5. if you are overweight, lose weight.
6. avoid alcohol.
7. consult a ENT surgeon if problem still persists.
Dr. Anil Jain