Update: readers will want to read the comments as well. There have been some very helpful insights/challenges posted there. S. Scott Bartchy’s article “Slaves and Slavery in the Roman World” in the recently published The World of the New Testament: Cultural, Social, and Historical Contexts addresses the legality of Onesimus’ flight to Paul from Philemon. He writes:
Not infrequently, knowledgeable slaves left their owner’s control temporarily to hide from an angry owner and wait for tempers to cool, perhaps hoping to find an advocate to intervene on the slave’s behalf. Others took off to visit their mothers (Dig. 18.104.22.168-5).* According to Proculus, the foremost Roman jurist of the first century, such a slave emphatically did not become a fugitivus (Dig. 22.214.171.124).* In light of this legal option, the fact that Philemon’s slave Onesimus did not take off for parts unknown but rather fled to Paul in prison strongly suggests that it is incorrect to regard Onesimus as a runaway slave (see Byron, Paul and Slavery, 116-37).* 
Elsewhere in this chapter he notes that whether or not a slave attempted to flee their master had much to do with how much they knew about the outside world. Sometimes if they thought they could escape to freedom they would do so, but this wasn’t always the best option. Slaves had very hard lives, but they were not the lowest social class: “impoverished free persons” were the lowest social class. Technically, a slave could do quite well being given “highly responsible and sensitive positions, such as managers of large farms, of households, of business enterprises and workshops, as well as physicians, accountants, personal secretaries, tutors, sea captains, and even municipal officials.”  Some slaves owned their own slaves (a sort of slave hierarchy) and they could accumulate a person fund. Often people sold themselves into slavery as a means of survival. In other words, better to live a slave than starve to death as an impoverished free person. 
When we read Paul’s letter to Philemon we may not find a Paul who is wildly supportive of slavery. In fact, his language suggests that he hoped that Philemon would consider his relationship to Onesimus to be more than that of slave-master. What we do find is Paul functioning in an acceptable social role as an advocate. Onesimus is not a fugitive because he fled to Paul. He did the proper thing. If Onesimus would have fled to escape he may have been treated far, far worse if caught and who is to say whether he could have survived if he had not been caught. Remember, slaves had it bad, but the “economy” functioned in such a way that slavery was the better option at times (Batchy notes that unlike the situation in the southern United States there was no “free north” to which a slave could flee). Paul himself was not a political or socially powerful man. He likely didn’t have the means to do much for Philemon, but because Philemon had come to embrace Paul’s Gospel this did give Paul a particular relational standing that allowed his to be Onesimus’ advocate. What we find in Paul’s epistle is Paul functioning in that role, doing what he can to soften Philemon’s heart, even nudging him to reconsider the nature of his relationship to Onesimus.
* Dig. = Digesta (Digests), and anonymous ancient work. Byron = John Byron, Recent Research on Paul and Slavery (Sheffield: Sheffield Phoenix Press, 2008).
 p. 172
 p. 173