There are a couple of different reasons why the faucet is leaking while it is turned off. One reason could be that the packing behind the packing nut is worn, or damaged. It could also be the seals on the stem. If the seals are damaged it will allow the water to pass through, and cause the faucet to leak. If the leak is not addressed, and fixed it will lead to the seat in the faucet being cut. If the seat is cut you will have to replace the complete faucet.
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