Preheat oven to 350°. Spread cornbread on a large rimmed baking sheet. Bake until cornbread is dry and starting to crisp, about 15 minutes, turning pieces over once halfway through; set aside. Keep oven on.
Heat oil, meanwhile, in a large frying pan over medium heat. Cook onion, stirring often, until golden brown and sticky, about 20 minutes. Transfer to a large mixing bowl. Add dried fruit.
Pour in broth, eggs, salt, and sage and mix well to combine. Add cornbread and toss gently just to moisten. Transfer mixture to a greased 9- by 13-in. baking dish.
Bake stuffing until it feels firm to the touch and the top is starting to brown, about 40 minutes.
Note: Nutritional analysis is per serving.