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Babette, on the other hand was probably out 'hunting' or gathering ingredients (due to the fact she is the Black Hand's resident alchemist and poison expert), completely missing the raid on the Sanctuary. Using in-game time, if the Dark Brotherhood is destroyed Cicero will never make it to the Sanctuary in time, discovering that he is probably the only Brotherhood member left alive and will hide back in the Dawnstar Sanctuary and rot to death with the Night Mother. No matter if you ignore him, help him, or hinder him, it will still take some time to get all the way to Falkreath with a load like the Night Mother on the cart. If you remember correctly, Cicero is currently on the road north of Whiterun waiting for his wagon wheel to be fixed. When you begin the 'Destroy the Dark Brotherhood!' quest, you would have to meet Astrid in the abandoned shack prior.
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Well, let's look at the technical side of this.
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