Using covert operation terminology, the phrase ‘terminate with extreme prejudice’ means to execute or assassinate the employee or said target. The term was explained by Terence Smith, a former reporter of The New York Times.
The reference is directed to the the Green Beret Affair, which is during the the Vietnam era from 1966 to 1970. Project GAMMA was the name of a (aka Detachment B-57 Company E, 5th Special Forces Group) special operations.
Intelligence had been compromised in Cambodia. Chu Van Thai Khac had allegedly met with North Vietnamese intelligence officers and supposedly there were pictures to prove it. An Ops officer and CIA headquarters decided that “elimination … might be the best course of action”. This was the option chosen, although the 5th Special Forces Group’s exec was against the killing.
The particular case involved the killing of Chu Van Thai Khac. “On June 20, 1969, three officers assigned to Project GAMMA drugged Chuyen, took him out on a boat into Nha Trang Bay, shot him twice in the head and dumped his body into the South China Sea.”
Eight soldiers were responsible for the murder and the case would go to trial, but the charges were dropped against the soldiers.
The 1969 article named “Details of Green Beret Case Are Reported in Saigon”, suggested that one either be isolated or ‘terminated with extreme prejudice’, a euphemism for execution.
The phrase plays upon another similar phrase ‘terminated without prejudice’, meaning the “fired employee may be rehired readily for the same or a similar job in the future,” which is usually true in the case of layoff.
If the employee is ‘terminated with prejudice’, it means an employer will not rehire the former employee to a similar job in the future. This is it for said employee.
Pink slips may include a set of check boxes where a supervisor can indicate ‘with prejudice’ or ‘without prejudice’.