Place the pork shoulder in the slow cooker. In a small bowl, stir together the chicken broth, brown sugar, chili powder, smoked paprika, garlic powder, salt, and black pepper. Pour the mixture over the pork.
Cover and cook on low for 8 hours or until the pork shreds easily with two forks.
While the pork cooks, make the slaw. In a medium bowl, combine the shredded cabbage, shredded carrots, mayonnaise, apple cider vinegar, and sugar. Stir well and refrigerate until ready to serve.
Once the pork is done, shred it directly in the slow cooker and stir it into the juices.
Warm the corn tortillas. Fill each tortilla with pulled pork and top with a generous scoop of slaw. Serve with lime wedges on the side.