For the rub, in a tiny bowl stir together the brown sugar, paprika, salt and pepper. Set it aside.
Peel the onions and quarter them (cut each in half, then cut those pieces in half). Place the onions on the bottom of your slow cooker.
Place the pork on top of the onions. Rub the brown sugar mixture all over the pork, making sure to cover all sides. Wash your hands well afterward.
Pour Liquid Smoke on top of the roast. Prepare the vinegar dressing in a liquid measuring cup. Add the vinegar, the Worcestershire sauce, then the remaining ingredients, and whisk to blend. Pour half of this mixture over the meat and cover and refrigerate the rest for later.
Cook the meat on low for 8-10 hours. Transfer the pork, onions and juices to a platter, add some of the reserved vinegar mixture, and shred the pork with two forks. (The vinegar dressing is spicy, so add it according to your taste.) You can have the remaining dressing at the table for each person to add more if they wish.
Serve the pork in sandwiches, burritos, enchiladas or over rice. Refrigerate leftovers for up to four days.