A hunter with survival skill above 75 automatically processes their daily yields, basically adding rations and leather instead of meat and skins, but they don't seem to touch existing stockpiles of meat and skins. I agree that it would be nice for one of the assignments to process those stockpiles, if one doesn't already - perhaps a skilled hunter could process a few extra units on top of what they brought in that day, or a hunter with no ranged weapon or no ammo could be assigned to processing full-time, or a Pantry Girl with survival skills could process a few units of meat per day.