Most of our contracts were for employees to give one months notice, unless otherwise stated. If anyone didn't work out their full notice & just 'left' before the due date, they would lose out on x amount of pay & a reference from me!
However, I was quite flexible if there were extreme reasons for employees needing to leave before the due date & usually came to an amicable arrangement.
Unfortunately, not everyone's so forthcoming, so it's best to have a very good excuse at the ready, but not just for moving on to another place of work!