Complex sentence: The detective found the house where Vincent was living, and the family wrote letters to her, but as she was already dead by this time, they received no response, and the family assumed that she had deliberately broken ties with them.
Split into simpler sentences: The detective found the house where Vincent was living, and the family wrote letters to her. But as she was already dead by this time, they received no response, and the family assumed that she had deliberately broken ties with them.