No you may not legally do this. Federal law requires you to pay every employee for all hours worked. Regarding state employment laws, even if you do not live in an employment-at-will state, no law requires employees to give you notice when they want to quit.
The most you can do to reduce the possibility of this occurring is to have promulgated policies in place that specify that accrued, unused vacation/sick time that might otherwise be paid upon termination may be withheld if proper working notice is not given by the departing employee.
Question added to topic Human Resources • January 20, 2009
Can I withhold a final check from an employee who quit with no notice?
An employee quit on me without notice. Can I decline giving him his last pay check?
Penny is a seasoned human resources executive and consultant with over 25 years of diverse business experience in advising enterprise leaders on employment-related matters.