Remove any ties from the pork shoulder and pat it dry with paper towels. Trim any excessively thick fat cap, leaving about ¼ inch for flavor.
In a small bowl, combine the spice rub ingredients. Rub the mixture evenly over the pork on all sides.
Spread the sliced onion across the bottom of the slow cooker. Place the seasoned pork shoulder on top.
In a small bowl, combine the apple juice (or broth), apple cider vinegar, and Worcestershire sauce. Pour the mixture around the pork.
Cover and cook on LOW for 8 to 9 hours or HIGH for 4 to 6 hours, until the pork is very tender, shreds easily with a fork, and begins to fall apart when you lift it. Start checking the pork toward the lower end of the cooking time to avoid overcooking (overcooking can result in mushy pulled pork).
Transfer the pork to a large bowl and let it rest for about 10 minutes. Shred the meat with two forks, discarding any large pieces of fat.
Pour the cooking liquid from the slow cooker through a fine mesh strainer into a bowl or measuring cup, discarding the onions.
Add about ½ cup of the defatted cooking liquid (instructions below) to the shredded pork and toss to moisten, adding more as needed.
Serve warm.