There isn't a firm answer to that in Jackson's films. In Tolkien's legendarium Beorn went on to become a great chieftain among the Men of the Anduin Vales (mostly, if not entirely, Woodmen); his followers named themselves the Beornings after him. Sometime after the Battle of Five Armies, Beorn wedded and had at least one child, a son named Grimbeorn (later Grimbeorn the Old). Beorn seems to have died by the time of the War of the Ring. It is reported that many of Beorn's male descendants were skin-changers like himself and could also take the form of great bears. It is not known whether that gift was ever inherited by any of the women of his line.