Luciano Fabbri was the Cuneo family's consigliere who was often known as 'the Fat Man' due to both his girth and status in the family.
He was known to have a wide knowledge of inter-family squabbles, and in 1950, began plotting for a war against the Corleones, despite the peace made several years before. Incidentally, Fabbri represented the Cuneo family at the wedding of Connie Corleone and Carlo Rizzi.
However, one morning, Fabbri made a stop at a hot-dog vendor whilst on his way to a meeting with Don Cuneo. At this point, the Corleone's enforcer, Aldo Trapani, executed Fabbri and his guards after taunting the consigliere. This hit was sanctioned by caporegime Peter Clemenza, who was known to have a hatred of Fabbri and his methods.
Fabbri's body was recovered and thrown into the East River. His demise soon became known to the Cuneo family, who, instead of calling off the attack, pressed it forwards and killed several Corleone soldiers.