In classical times, the Greeks' tragic heroes were always "great men" in terms of their status and even their character, but they were brought down by a tragic flaw (or tragic mistake, fate, etc.). Today, we always think in terms of a tragic character flaw but not necessarily that a tragic hero cannot be an ordinary person or of ordinary status. Does Fences meet the criteria of a tragedy in the latter sense? If you think so, who is the tragic hero, and what is the hero's tragic flaw? What downfall does the tragic hero meet?

Yes, in classical tragedies like those by Ancient Greek playwrights like Sophocles, the tragic hero would have been a high-ranking member of society. For example, Oedipus is the king of Thebes, and the other major characters like Creon and Jocasta are also royalty. This tradition continued with Shakespeare's plays, in which his tragic heroes were usually monarchs or members of high-ranking families. It is also true that in modern American drama, the protagonists do not have to be powerful people, wealthy people, or people who rule over others. August Wilson's Fences portrays one such tragic hero in Troy Maxson.
Troy is a member of the working class who lives a modest life, though he once had ambitions to rise in the world through his skill at baseball. His failure to achieve that potential results in one of his flaws, which is his bitterness and his sense of being wronged by fate and/or his circumstances (especially racism). In the current time of the play, Troy is a middle-aged man who still isn't over feeling cheated by the world around him, and he takes that out on his wife and especially on his son, Cory. The relationship between Troy and Cory is marked by tension, as Troy disapproves of Cory playing football. He believes the same forces that held him back will also conspire to ruin his son's chances for a better life. He doesn't seem able to recognize that things may have changed or to allow his son to learn and strive on his own. Part of this is Troy being protective of his son, since Troy was so hurt by the discrimination that hindered his own potential; Cory, however, thinks his father is jealous of Cory's chance at success (which links back to Troy's bitterness).
In his relationship with his wife, Rose, Troy is unfaithful and doesn't seem to fully appreciate all the ways his wife takes care of him and the family. Troy's bitterness and feeling that he is a victim leaks into his marriage as well. Rose is very compassionate and even agrees to raise Troy's illegitimate child with Alberta. However, Troy's philandering ways do change Rose's feelings toward him.
In the end, Troy's character seems tragic because he had so much potential, but he let his sense of self and his will to truly live die with his hopes for playing major league baseball. He is not resilient and cannot find happiness or contentment in ordinary life after feeling wronged by the racist society around him. The audience can both understand how Troy feels and wish that he had somehow been able to rebound and build a meaningful life with Rose and Cory.