In a 4-6 quart slow cooker (mine is a 6.5 quart and it turned out great), combine the beans, sausage, onion, celery, and thyme. Add the broth and stir to combine.
Cover and cook until the beans are tender, on LOW for 7 to 8 hours or HIGH for 4-5 hours.
minutes before serving, remove and discard the thyme sprigs and add the collard greens. Cover and cook until the greens are tender, about 15 to 20 minutes. Stir in the vinegar and salt and pepper to taste.
Drizzle with olive oil, if desired.