In a Dutch oven, melt the butter over medium heat. Add the onion and cook until softened, about 3 minutes. Add the garlic and cook just until fragrant, about 1 minute more.
Stir in the chicken stock, lima beans, corn kernels, diced tomatoes with juice, barbecue sauce, Worcestershire sauce, celery salt, black pepper, and cayenne pepper.
Bring the mixture to a boil, then reduce the heat to a simmer and let simmer uncovered for 15 minutes. Add the pulled pork and chicken and simmer for an additional 15 to 20 minutes or until the stew is thickened.
