Pour the oil into the bottom of a slow cooker. Place the pork roast into slow cooker; pour in barbecue sauce, apple cider vinegar, and chicken broth. Stir in the brown sugar, yellow mustard, Worcestershire sauce, chili powder, onion, garlic, and thyme. Cover and cook on HIGH until the roast shreds easily with a fork, 5 to 6 hours.
Remove roast from slow cooker and shred meat using two forks. Return the shredded pork to the slow cooker, and stir meat into the juices.
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