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Boxwoods are very resilient. I've had them die almost to the ground and come back. Those dead branches won't grow new leaves because they are dead. Cut them out and eventually, the middle will fill in.
You don't say where you live but if its an area that has cold dry winters, you may have to water a few times during the winter.
Always make sure all your soil is good and damp before the ground freezes. Cold dessicates plants.
