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A couple of stories said Pilate fell out of favor with Rome and was forced to kill himself. One, however, said Pilate and his wife Claudia later converted to Christianity and were martyred.

FWIW, I came across the following:

The Mystery of Pilate's End

Pontius Pilate is known to have been a Roman governor of Judaea from about A.D. 26-36, which is a long tenure for a post that normally lasted only 1-3 years. Maier uses this observation to support his concept of Pilate as a less than awful prefect (Praefectus Iudaeae). Pilate was recalled after he was said to have slaughtered thousands of Samaritan pilgrims (one of the four incidents of maladministration). Pilate's fate would have been decided under Caligula, since Tiberius died before Pilate reached Rome. We don't really know what happened to Pontius Pilate -- other than that he was not reinstated in Judaea. Maier thinks Caligula used the same clemency he used for others accused under Tiberius of treason, although popular versions of what happened to Pilate are that he was sent into exile and committed suicide or that he committed suicide and his body was tossed in the Tiber. Maier says Eusebius (4th century) and Orosius (5th century) are the earliest sources for the idea that Pontius Pilate took his own life. Philo, who was a contemporary of Pontius Pilate, does not mention a punishment under Caligula or suicide.

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