So what you are trying to do is dissolve the chewing gum from a mixture of gum, sugar, drug, etc., which is actually designed to have the sugar, drug, etc. dissolve in saliva while leaving the gum base behind?
Perhaps you could put the gum in hot/boiling water until everything but the gum base dissolves, filter/decant the resulting solution and then dehydrate (boil? let sit until it evaporates?).