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In my personal experience NO Staffie's do not drool after long walks over the years i have owned 6 staffies and none of them drooled.
Speaking of food, it is not uncommon for a puppy or dog to drool in anticipation of food. The eyes see the food, it sends a signal to the brain and the salivary glands kick into action before the food passes by the lips; therefore just the sight and thought of food triggers the glands to work.