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The broker is required to sell the stock at or above the stop limit order price, if and only if, there is a willing buyer who will pay the limit order price. Should the market price of the stock fall well below the stop limit order price (this is considered a "gap down" ), then, although your stop limit order has been activated, it will not fill unless the market price of your stock rebounds back to or above your limit order price.

Once the market price of your stock has plummeted below your limit order stop loss price, it could continue to move lower (even to zero) and your limit stop loss order will never fill.