Employees who threaten to quit usually want something other than their employer's acceptance of their resignation. They might be looking for recognition for their performance or accomplishments or they could be fishing for a retention bonus based on how much the company values their contributions. Your options include waiting for the employee to actually quit, accepting the employee's threat by firing her or experimenting with other ways to satisfy the employee's need for attention or recognition.
Given the employment-at-will doctrine, you can fire an employee for any reason or for no reason, with or without advance notice. The employment-at-will doctrine permits private-sector employers to sever the employment relationship at any time. Therefore, if you have an employee who repeatedly threatens to quit her job, you have the right to terminate her. That being said, there are exceptions to the rule.
You will have a difficult time firing an employee with whom you have an employment agreement. An exception to the employment-at-will doctrine says that employers cannot exercise their rights under the employment-at-will doctrine if there's an employment agreement or contract in force. To fire an employee who threatens to quit, you need to adhere to the terms and conditions of the employment contract and some contracts require 30- to 60-day notice in writing.
Another exception to the employment-at-will doctrine relates to public policy. When an employee exercises his rights pursuant to public policy, many states recognize that as an exception to employment at-will, which means an employer cannot fire someone who files a workers' compensation claim, supports labor organizing activity, blows the whistle on an employer's wrongdoing or testifies against the employer in legal proceedings.
Although you might tire of the employee's repeated threats to quit, calling his bluff might not be in the best interest of the company because the employee may construe it as a wrongful termination. Following termination, employees usually file a claim for unemployment benefits and in cases where the employer appears to have terminated an employee without a reasonable cause, the employee could be eligible for unemployment benefits.
A workplace policy that prohibits behavior that damages employee morale or that conflicts with the employer's philosophy and values may be the answer to your problem. Provided you have such a policy and that you can see the effects on other employees, warning the employee each time she threatens to quit could drive home a message that you won't tolerate the continual threats to resign.