Place the pork shoulder in the slow cooker. Add the sliced onion, minced garlic, chicken broth, and taco seasoning. Season with salt and pepper.
Cover and cook on low for 8 hours until the pork is very tender and shreds easily with a fork.
While the pork cooks, prepare the slaw. Combine the shredded cabbage, shredded carrot, mayonnaise, and apple cider vinegar in a mixing bowl. Season with salt and pepper, then stir well. Cover and refrigerate until serving.
Once the pork is done, shred it directly in the slow cooker using two forks. Stir the meat into the cooking juices.
Warm the corn tortillas. Fill each tortilla with pulled pork, top with cabbage slaw, and finish with fresh cilantro and a squeeze of lime.