When an employee chooses to leave an employer, he will often, as a matter of courtesy, provide the employer with at least two weeks' notice before his date of departure. Generally, the employer will use this period of time to find a new employee. However, the employer will not generally have any legal obligation to keep the employee on for two weeks. The employer is generally allowed to fire the employee before this time.
Two Weeks' Notice
When a person gives two weeks' notice, it is generally done as a matter of politeness rather than for any legal reason. Indeed, the "two weeks" length is a matter of convention; it is not grounded in any legal statute. When notice has been given, the employer's relationship with the employee does not change. He can fire him for the same reasons he could before notice was given.
Whether an employer is allowed to fire an employer will depend on a number of different factors, including the reason that the employee is being fired and the conditions under which he was hired. Most employment law is made at the state level, and federal law provides no protection to individuals who choose to give their boss notice. In few cases will a law protect a notice-giving employee.
At Will vs. Contractual Employment
If a person is employed at will -- meaning he can quit whenever he wants and he can be fired whenever his employer wants -- there is no reason that his boss cannot fire him before his two weeks are up. However, if the employee's job is secured by a contract, his boss can only fire him if doing so does not violate the contract's terms.
Before firing an employee, an employer should consult with an employment attorney to determine how to do it legally and with a minimum chance that he employer will face a lawsuit over wrongful termination. While an employer may legally be allowed to fire an employee before his two weeks are up, it will likely engender bad blood and may raise the chances of the person filing a lawsuit against his employer.