The judges' hit man
The movie never explained the Star Chamber's hit man or how the system worked. True, one may say that such explanation would have been only tangential to the movie and superfluous. I still would have liked to have seen some details on how it all worked out. What kind of 'hit man' did the judges employ? Was it a mafiosi-type? Was he a former military man from a highly-trained specialty, say, the Special Forces? Was he a free agent like Charles Bronson's character in, 'The Mechanic'? The last one is most likely.
I agree with another OP. The judges should have arranged some kind of, 'recall' or, 'abort' signal to the hit man in the event there was a mistake. The judges' mistake was to presume they would never make a mistake selecting a criminal for termination. The judges were afraid of any remote possibility they could be connected directly to the hit man.
This movie is another angle taken from, DEATH WISH, but at a much higher level of society and sophistication. It plays upon the frustrated public's desire for justice. There was a Stallone action movie from the 80s where his character is a street cop from a large metropolitan police department that harbors a secret group of cops, nicknamed, the zombie squad, whose task is to carry out liquidations of dangerous criminals and thugs that escape the justice system.
Herein lies the frustration of the American people. We have dreaded for so long the peversion of law and justice through corruption and politics that our nation tried to construct a fool-proof legal system to prevent the innocent from being illegally 'legally' harmed. In consquence the real criminals have can appear to have too much or unmerited protection. The worst are those on death row waiting for their executions for 20 years sometimes. While we fear for those on death row who might actually be innocent and framed by criminals or even corrupt cops, just about all have been convicted with singularly convincing material evidence; caught in the act of homicide; some even boasting of it such as gangbangers. These need not wait 20 years.