Why would the witnesses have brought the case to begin with?
In Anglo-American law the State (Crown, whatever – in the US, the local public prosecutor) brings the case and summons witnesses (sometimes against their will), and coerces them to testify in many cases.
The word “witness” in English implies a bystander with information based on what they saw. The Hebrew word ??? should probably be translated more as “accuser” as the role of the ??? is similar to that of a grand jury or public prosecutor in that the ??? initiates the criminal proceeding.
Also note the Jewish courts can receive and use information from persons who do not have the status of ??? whereas an Anglo-American court can not based in decision on the facts from someone who isn’t a “witness”.
So if two Jews give warning and witness the murder of someone, for a non-controversial example, a Nazi war criminal, and then decide that the murderer was justified in killing the Nazi, there is no requirement for them to go to Beis Din a initiate a criminal proceeding – though under American law the witnesses would be accessories if they didn’t report the murder of the Nazi, though the Prosecutor could dismiss the case “in the interests of justice” (at least under Anglo-American law, some Roman-law based systems require the prosecutor to proceed on all complaints).