Place the pork shoulder in the slow cooker. Add the sliced onion, minced garlic, chopped figs, balsamic vinegar, and chicken broth around the meat.
Cover and cook on low for 8 hours until the pork pulls apart easily with a fork.
About 45 minutes before the pork is done, preheat the oven to 425 degrees. Toss the potato pieces with olive oil, rosemary, thyme, salt, and pepper in a large bowl.
Spread the potatoes in a single layer on a baking sheet. Roast for 35 to 40 minutes, stirring once halfway through, until golden and crisp on the edges.
Shred the pork directly in the slow cooker and stir it into the sauce. Serve the pork over or alongside the roasted potatoes.