He got shot.
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Tom didn't try to escape the courtroom. In Chapter Twenty-four, we learn that the day Tom went to prison, he lost hope. Atticus couldn't promise Tom an acquittal so he didn't try to reassure Tom by giving him potentially false hope. Atticus later entered the house and requested Aunt Alexandra and Calpurnia's presence in the kitchen. He revealed that Tom tried to escape from prison and was shot to death by the prison guards. Apparently the guards tried to tell him to stop and fired warning shots, but Tom kept running.