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In an at-will employment state, any employee can be terminated at any time for any reason that is not against the law or discriminatory, or because of harassment based on discrimination. A reason that is against the law would include, for example, an employee being terminated because they refused to illegally dispose of hazardous waste. A discriminatory reason, or harassment because of a discriminatory reason, arises from a termination because an employee is in a protected class. A protected class includes race, religion, national origin, and so on. More information about that is available at www.eeoc.gov.
That being said, there are exceptions to at-will employment. Those include:
Other than that, an employer does have a right to terminate an employee, even if it leaves the job open and the employer has to hire a new employee.