First, a rule regarding broken sticks:
10.3 Broken Stick – Player - A broken stick is one which, in the opinion of the Referee, is unfit for normal play.
A player without a stick may participate in the game. A player whose stick is broken may participate in the game provided he drops the broken stick. A minor penalty shall be imposed for an infraction of this rule.
A player who has lost or broken his stick may only receive a stick at his own players’ bench or be handed one from a teammate on the ice. A player will be penalized if he throws, tosses, slides or shoots a stick to teammate on the ice. A player may not participate in the play using a goalkeeper’s stick. A minor penalty shall be imposed for an infraction of this rule.
A player tendered a stick thrown on the ice from the players’ or penalty bench will not receive a penalty. However, the person responsible for throwing the stick will receive a bench minorpenalty.
I couldn't procure a camera, so I ended up taking this video from my computer's webcam. Also, I couldn't find a good still frame, but you can see Patrice Bergeron's stick breaking and then advancing the puck:
The quality is terrible. Sorry.
You can see the stick snapping just before the 'pass' is made across the goal mouth.
Bergeron got away with one.
*EDIT* I have had some people tell me that a puck that advances while a stick breaks is allowed. I contend that, though the quality of my video is shit, that the stick broke off of PK Subban's stick before contact with the puck was made. The still image shows his stick at a near 90 degree angle taken before contact with the puck.