Season the ground beef with half the salt and pepper, then roll it into small meatballs, about a tablespoon each.
Cut the cabbage into thin strips.
Add the chicken breasts, meatballs, drained tomatoes, and sliced cabbage to the slow cooker. Sprinkle in the remaining seasonings, then pour the chicken stock over everything.
Cook on low for 7 to 8 hours or on high for 4 to 5 hours.
When the soup is done, use two forks to shred the chicken right in the slow cooker and stir everything together.
Ladle into bowls and top with avocado, lime, cilantro, sour cream, or shredded Mexican cheese.