Fabbro was a healthy scratch 9 times this season, and only played third pair minutes. Last season the Predators only played him in 56 games, and scratched him for three playoff games. There is some promising data around Fabbro, but it seems that the Predators have lost trust in him as an NHL player - and they're closest to the player.
The Oilers may have believed in Fabbro enough to place a claim on him, but taking his full $2.5M salary likely would mean that he would essentially be the team's trade deadline acquisition. Fabbro may turn out to play up to his potential in Columbus, but it still would've been a major risk for the Oilers to claim Fabbro.