Deuteronomy 23:15 If a slave has taken refuge with you, do not hand them over to their master.
Paul knows this.
Philemon 1:8 although in Christ I could be bold and order you to do what you ought to do, 9yet I prefer to appeal to you on the basis of love. It is as none other than Paul—an old man and now also a prisoner of Christ Jesus— 10that I appeal to you for my son Onesimus, who became my son while I was in chains. 11Formerly he was useless to you, but now he has become useful both to you and to me. 12I am sending him—who is my very heart—back to you. 13 I would have liked to keep him with me so that he could take your place in helping me while I am in chains for the gospel.
It seems that the decent thing for Philemon to do is to release Onesimus to Paul's charge. Since Philemon is from Colossae, Paul writes a separate letter to the Colossian church at the same time.
Philemon and his family lived in Colossae, and the Colossian church met at his house. Paul wrote his letter to the Colossians at the same time he wrote to Philemon. In that letter, Paul mentioned that Onesimus would be coming home. Paul gave both letters to Tychicus and Onesimus to carry back to Philemon (Colossians 4:9).
What was the outcome after Onesimus had returned to Philemon in Colossae?