God always has a purpose in all He does or allows, but only arrogant people assume they understand the full picture.  Paul is more tentative.  He suggests that part of the reason for Onesimus leaving Philemon's service was that he needed to encounter Jesus before he could be a help rather than a hinderance in Philemon’s house where the Colossian church met.  He could have heard the gospel and responded under Philemon’s teaching but that did not happen.  Perhaps Onesimus was previously resentful of his role and of Philemon's Christian convictions, or that Philemon was a harsh master.  But the pivot point in their stories was that the run-away slave found Jesus (Philemon 1:10) ... and he was changed.

The forgiven sinner learnt how to serve from the heart (Philemon 1:11).  In fact, he was so useful that Paul was depriving himself by sending Onesimus back. The slave had a changed heart; what he thought was a move to get his own way proved to be a move in which God would change his way. Now Paul wanted Philemon to open his home to the repentant returnee, as a member of the family of Jesus - not just a better slave but a fellow human being, child of God and brother in Christ.

The way in which Paul writes implies that Philemon might not be so welcoming; Paul appeals to Philemon to listen and act in generous forgiveness (Philemon 1:9-10).  Even if he will not do so because of the previous bad relationship with Onesimus, Paul begs him to show mercy and receive him back because of his respect for Paul’s apostleship (Philemon 1:17-19), or for the partnership relationship they have enjoyed in the past (Philemon 1:6, Philemon 1:17)

Like the prodigal son (Luke 15:11-32), God can allow people to move away so that they wake up to spiritual reality, repent and come back to become useful.  But they need to move back as changed and reformed people. That is the essence of repentance.  All too often we hear about the need to 'move on', which means boldly assuming a new start but rejecting the need for repentance.  That is a spiritual deception, alas encouraged by sentimental believers who have little concept of righteousness.  In every move, which the Lord precipitates, you will find His change-agenda.  Allow Him to do His work and then go back to show what the Lord has done for you.