They can decide to quit their job at any time, for any reason, or for no reason. Likewise, the employer can also decide to let an employee go for any reason, or for no reason, without liability. Employment for a specified term means an employment for a period greater than one month.
Individuals are generally upset after being fired, and understandably so.
In many situations, however, no matter how painful the experience, and no matter how bad the employer treated the employee in terminating them, there is no legal recourse for the employee. Even if the employer lies about the reason for termination, the employee has no claim. This is the most common exception to the general rule. This exception is so common that it could almost said to be the general rule, with at-will employment status being the exception. This type of agreement can be written, oral, or implied.