Esau is a character mentioned in Dead Island. He's never actually seen in game, however he is mentioned by Tim in the Church.
He is a criminal based in Moresby who was suspected of raping and killing the wife of Tim. However, he was not convicted, as people were too afraid to testify. Tim vows to kill Esau, and gives the Hero two side quests in order to prepare for his revenge.
In order for Tim to carry out his revenge, he first needs the detective's files on the case from the Police Station. As the case had a lot of damning evidence on Esau, the file was large and yellow, left on the desk of the detective who worked on the case.
Once Tim had the file, he just needed a gun to carry out his revenge. He knew that his neighbour had a gun and never got to it before being mauled and killed by the zombies. As such, he requests that the hero goes and retrieves the gun so that Tim can carry out his long awaited justice and give Esau his final (death) sentence. It is likely that he was hunted down by Tim, but this is never confirmed, as he could have either escaped the island or become infected before Tim finds him.