Is being fired in fury forever?
The halachos of mechilah (lit., forgiving, i.e., absolving someone from an obligation) do not entail a kinyan (act of acquisition) as do most other transactions; verbalizing intent suffices. (See Halachah # 678 for details).
An employer who said to a worker “lech me’imadi” (“Depart from me!”) can have no complaints against the employee for quitting, nor for the resultant losses—of work and of money—even if the entire salary had been prepaid, since the employer voiced mechilah of their work contract. Two witnesses are needed for the mechilah to be binding if the dismissal is in dispute.
However, if a melamed (Torah teacher) was fired and left (even with a written mechilah, according to most poskim), he can be compelled to return to his post. A melamed is duty-bound to his students in addition to the (now defunct) obligation to the parents, unlike any other employer/employee relationship. (There are some exemptions to this arrangement for the teacher’s reinstatement: if another melamed is immediately available or if the melamed was fired for incompetence. If the melamed isn't employed by the parents, but through a third party—and this applies today in a school or yeshiva environment—this halachah may not apply.)
A mechilah b’ka’as (release from an obligation made in anger) can be retracted if the employer regrets his reaction in the heat of the moment. Some poskim disagree, and maintain that the irate boss is bound to the sacking statement. However, the mechilah is valid only if the firing was obviously made with intent (as opposed to mere bluster), such as if it was said in the presence of witnesses or if it took place in front of a Beis Din.
The ticked-off taxi-driver who yells (over the screech of tires) to a recalcitrant passenger, “Get out of my cab and take your fare with you!”, is not considered to have conferred true mechilah and the fare must be paid.