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It depends on the faucet and whether the faucet has an aereator. Even when the valve is turned into the off positions, there is still some residual water in the faucet, and aereator. Once all of the water on the room side of the faucet has drained out, the dripping will stop.
If you have not done so already, it helps to drain the system at the lowest point. Meaning apply the shut off valve first, open the faucet at the lowest point (usually in the basement or hose bib) so the system can drain, then open a faucet at the highest point. This will allow air into the system and allow it to drain more quickly. Much like releasing your finger off the top of a full drinking straw.
We hope it helps!
Both of the previous are great ideas. Also consider, if it is an older valve, that the main does not close completely, for a variety of possible reasons. We see that alot in older homes. You can confirm this by checking other fausets to see if they continue to drip after you have tried the above proceedures.
Remember if you drain the system as suggested before, to properly refill it, to get rid of the air in the system, or you could have "water hammer" issues as well.
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