Ian White ran out of luck.
When you break your stick in hockey, you become helpless. It's like if a pitcher lost his throwing arm in the middle of a game. (Try not to picture that, actually.) With the way they're made these days, you never really know when your stick is going to just shatter into pieces all over the ice. You can only hope that it happens away from the play and doesn't put your team in a bad position.
Ian White had no such luck. Or if he did, he certainly ran out of it at a terrible time. Just as the Detroit defenseman tried to pass from behind his own net, his stick betrayed him, snapping at the blade as the puck slid right in front of the net.
I'll give White credit for his desperate slide to try to intercept the pass from Matt Beleskey to Corey Perry, but honestly at that point Jimmy Howard was the only one who could bail his team out of the situation. He couldn't, and the Ducks tied it up.