The Reverse cases are Personae related murders that take place in Ayanagi during the events of Persona -Trinity Soul-. Ayanagi police superintendent Ryou Kanzato has been hiding all information on this cases from the public.
Method
The Reverse cases are caused when a Persona is forcefully extracted from it's user. A successful extraction results in the victim being turned inside out, which is why the police had dubbed them Reverse cases. Following Mariya Kujou and Ryou Kanzato's fight, Mariya falls into a coma, which causes the Reverse cases to cease.
Purpose
The reason behind extracting Persona is so that those persona can be consumed by Marebito Personae. This increases the strength of Marebito's Personae, but makes them more unstable. While most of Marebito believe that this is to make them more powerful and to obtain a new level on consciousness, in reality, Mariya was gathering Personae in an attempt to resurrect his daughter.