I am quite sure I have never preached about Philemon. I know the story, but digging into it for a relevant interpretation was a good learning experience for me. Here is some history:
Onesimus probably was a slave, but doubtfully one who had run away. House arrest was common in Rome. If Paul had been behind bars, it would have been difficult to build a relationship with Onesimus, which the text clearly indicates has happened. Philemon had likely even sent Onesimus to support Paul, given Philemon’s history with Paul. That beautiful text from Matthew 25:36 reminds us how Jesus feels about extending ministry to those who are in prison. During this assignment, it seems that a moment of transformation transpired between Paul and Onesimus, a transformation in relationship that Paul describes by saying that Onesimus has become a child of his heart. Paul then calls for Philemon to refresh his heart (v. 20). What else could this mean than for Philemon to welcome Onesimus into his household as if Onesimus were Paul himself?
Another important point is that Paul expects this letter to be heard by the whole community even as he turns to Philemon directly in his request. Paul is calling upon the witness of the whole church in Philemon’s house to ensure that Paul’s hopes are fulfilled. Sometimes, when facing difficult circumstances, it is helpful to have friends who can hold us accountable to follow through with the intentions we desire. Whether Philemon desired to incorporate Onesimus into his family as a brother, we don’t really know. We do know, based on what Paul understood from the Reconciling love of Jesus, that Philemon was expected to issue love and forgiveness to his former slave.