While it's not about a town bully, it does feature a group of men who plot and carry out the execution of a soldier named Eddie Slovik, who was court-martialed and executed for desertion during World War II.
Here's why it might seem similar to the scenario you described:
* Unpopular Figure: Eddie Slovik was disliked by many soldiers due to his actions and was considered a coward.
* Group Decision: A group of soldiers, led by a Sergeant, decided to execute Slovik themselves after the official execution was delayed.
* Revenge/Justice: The men felt justified in taking Slovik's life as they believed he deserved punishment for his actions.
However, it's important to note that the film is a fictionalized account of Slovik's story, and the events depicted in the film are not based on real-life accounts.
Do you have any other details about the movie you're thinking of? Perhaps the time period or the actors involved? This could help me narrow down the search and find the correct title.