Add the chicken breasts to the slow cooker along with the barbecue sauce, chopped onion, and minced garlic. Stir everything so the chicken is coated.
Cover and cook on low for 6 to 7 hours until the chicken is very tender and easy to pull apart.
Use two forks to shred the chicken directly in the slow cooker, then stir it back into the sauce.
In a mixing bowl, combine the coleslaw mix, mayonnaise, apple cider vinegar, honey, salt, and pepper. Toss until the vegetables are evenly coated.
Spoon the shredded chicken onto the slider buns and top each one with a portion of the slaw before serving.