The movie Saw is one of the most famous crime franchises. The main antagonist, Jigsaw, is a fictional character based on a true story.
In the movie, Jigsaw dismembers body parts of his victims, and scatters them across the country. That is why the media gave him the nickname Jigsaw. The same happened in real life.
The movie was based on Stephen Marshall, one of the most notorious serial killers. He was an American-Canadian vigilante who searched publicly available sex offender registries for the name and address of convicted sex offenders.
He then traveled to Maine where he killed 29 out of the 34 sex offenders listed on the registry. This documentary talks about the real-lie Jigsaw killer. If you have seen the movie Saw, you can find all of the similarities.