Trim excess fat from pork. Heat oil in 10-inch skillet over medium-high heat. Cook pork in oil about 10 minutes, turning occasionally, until brown on all sides. Sprinkle with salt and pepper.
Place onion and garlic in 3 1/2- to 6-quart slow cooker. Place pork on onion and garlic. Pour broth over pork.
Cover and cook on low heat setting 8 to 10 hours or until pork is tender. Reserve 1 cup cooking liquid.
Serve pork now, or remove pork from slow cooker and cool slightly. Shred warm pork, using 2 forks. Place 2 cups shredded pork in each refrigerator or freezer container. Add 1/2 cup reserved cooking liquid to each container. Cover and refrigerate up to 4 days or freeze up to 4 months. To thaw frozen pork, place container in refrigerator about 8 hours.