Well, if oyu talk about exchange, it does NOT depend on broker. The broker and exchange will not. The order is in, can get executed. Cancelling an order is always the responsibility of the trader.
Now, the backend or the software may do so (like Ninja can etc.), but that is a "client side" implementation, and as such open to all kinds of issues (connectivity loss between orders etc.). Many trading packages have the logic for that built in.