Tom Robinson was shot in an escape attempt because he could not get over the fence fast enough with one arm.
Tom Robinson was naturally depressed when he was convicted. Atticus told him they had a chance on appeal, but he did not want to wait. Tom was tired of having no control over his own existence, and decided to make a run for it.
"They shot him," said Atticus. "He was running. It was during their exercise period. They said he just broke into a blind raving charge at the fence and started climbing over. Right in front of them-" (ch 24)
Of course, Tom Robinson was innocent. Yet he was persecuted for months, sat in jail, convicted after being proven innocent, and then sent to prison. It’s really no wonder he had no faith in the system. He just wanted it to be over.