In a small bowl, mix together the smoked paprika, garlic powder, onion powder, and black pepper. Rub this spice mixture all over the pork tenderloin.
Place the seasoned pork in your slow cooker. Pour the chicken broth and apple cider vinegar around the pork.
Cover and cook on low for 4 hours, or until the pork is tender and easily shreds with a fork.
Remove the pork from the slow cooker and shred it using two forks. Discard most of the cooking liquid, leaving about ¼ cup.
Return the shredded pork to the slow cooker, add the BBQ sauce, and stir to coat evenly. Cook on low for an additional 15-20 minutes to heat through.
Serve ½ cup portions (about 350 calories) over coleslaw or with a small whole wheat bun if desired.