Heat a stockpot over medium heat and add bacon. Cook until bacon begins to brown, 3 to 5 minutes. Stir in onion and garlic. Cook until onion is transparent, 5 to 7 minutes, stirring occasionally. Stir in broth, salt, black pepper, and cayenne pepper. Bring to a boil, about 5 minutes.
Stir cabbage into stockpot. Simmer until cabbage has wilted, 10 to 15 minutes. Stir in stewed tomatoes and liquid. Return soup to a boil, about 5 minutes. Cover and simmer, 15 to 30 minutes, stirring often.