Line a 9- by 13-inch baking pan with foil and place the pork in the pan. In a small bowl, combine the chili powder, salt, and cayenne. Rub the mixture over all sides of the meat, pressing it to adhere (if the meat is tied together with twine or netting, just rub the seasoning right over it). Set aside.
In a large skillet over medium-high heat, warm the oil. Add the pork and brown on all sides, 6 to 8 minutes. Transfer the meat to a slow cooker.
Add the broth to the skillet, scraping up any browned bits. Add the broth to the slow cooker, cover, and cook until the pork is very tender, 6 to 8 hours on low or 4 to 5 hours on high.
Transfer the meat to a cutting board and let rest 10 to 15 minutes. Use two forks to shred meat into bite-sized pieces. Moisten/season with cooking juices to taste.