I used to have a problem with my carb leaking after I would shut the egine off. The problem was with the needle and seat. I went through several suppliers before I found a vender with a very good quality needle and seat. My problem was solved, no more dripping carb. Mitch is correct that it is important to have a properly functioning needle, seat and properly adjusted float.
I rarely ever run the carb dry. I do however, turn the gas valve off as a precaution that something might leak when the car is parked.