What refers to a legal doctrine that specifies that the employer or employee can terminate employment for any reason?

Overview

At-will employment refers to an employment agreement stating that employment is for an indefinite period of time and may be terminated either by employer or employee. If an employment is at-will, such an agreement would typically be expressly included in the relevant employment contract. 

Exceptions

Even if an employment agreement contains an at-will provision, there are certain reasons as to why termination could still be wrongful. These exceptions will typically vary by state.

Public Policy Exception

The public policy exception bars an employer from terminating employees in violation of well-established public policy of the state. As an example, in many states an employee may not be terminated for filing a workers' compensation claim after an on-the-job injury.

Many states do not allow employers to terminate employees for refusal to violate the law at the employer's request.  Criteria for what violates public policy in a particular state varies from state to state. 

Implied Contract Exception

The implied contract exception means that an employee may have an expectation of a fixed term or even indefinite employment based on something the supervisor has done. This can take the form of employer's statements, an employer’s practice of only firing employees for cause, or an assertion in the employee handbook that specific termination procedures will be followed.

Implied Covenant of Good Faith and Fair Dealing

Some states recognize an implied covenant of good faith and fair dealing in employment relationships. Under this exception, an employer typically may not terminate an employee in bad faith or terminate an employee when the termination is motivated by malice.

Further Reading

For more on the at-will employment doctrine, see this Nebraska Law Review article, this Florida State University Law Review article, and this Monthly Labor Review article.

What is the term for the ability of an employer or employee to terminate?

In United States labor law, at-will employment is an employer's ability to dismiss an employee for any reason (that is, without having to establish "just cause" for termination), and without warning, as long as the reason is not illegal (e.g. firing because of the employee's race, religion or sexuality).

What is the doctrine called where either party employer or employee may terminate his her employment relationship at any time and for any reason?

At-will means that an employer can terminate an employee at any time for any reason, except an illegal one, or for no reason without incurring legal liability.
An ending of employment (such as a layoff) that is not a voluntary resignation. employment. labor law.

What is the doctrine that states that employers may not fire?

Fast facts about the at-will employment doctrine In the most basic sense, at-will employment means that an employer can terminate an employee for almost any reason — although a few exceptions to the rule may exist under state and federal law.