Preheat the oven to 400°F (200°C). Place the rack slightly below the center of the oven.
Place the pork in a casserole that is just large enough to hold it and has a lid.
Sprinkle the roast on all sides with worcestershire sauce. Then press brown sugar coating on all sides of the pork. Pour the apple juice down the side of the casserole to the bottom, being sure not to drizzle it on the crusted meat. Cover tightly.
Place the roast in the oven and immediately turn the heat down to 200°F (95°C).
Roast without opening the oven door for about 5 hours, until the meat is so tender that it pulls apart easily. If the meat does not pull apart easily, cover, and return to the oven and roast 30 minutes more. Check again, roast 30 minutes more as needed.
Pull the meat apart and remove the bone. Stir the salt into the juices at the bottom of the pan. Serve meat in its delicious juice hot or at room temperature.
Note: This can easily be done in a slow cooker. Set it on high for 30 minutes, then turn down the heat to low, and let it cook for most of the day or even overnight.
You can also pour off most of the juice if preffered and stir in your favorite bbq sauce after shredding. Heat through in pot on the stove over medium-low heat.
This should make about 12 sandwiches.