Mostly we find old people sleep open mouth but even some younger people also sleep with open mouth. This is due to problem in breathing. as they couldn't have proper breath from nose at night time so they take breath from mouth also
We generally sleep with open mouth when the oxygen requirement of the body is more and the nose is not sufficient to supply the required amount of oxygen. This is more found among the aged because they seem to be very tired and and their lungs needs more oxygen hence it happens automatically....!