The boss should be the last to go leave the office or workplace. Staying back would allow you to check all the record books and find out any irregularities and things you need to correct...
When I worked in a pleasure toys company some years ago, my boss doesn't come to work all the time. Whenever he's around, he doesn't stay till we close shop. What he made us to is to send the day's sales report file for him to go through before giving us a go head with leaving.