I read case law on this in a few cases where state level cops had impersonated the FBI in order to get defendants to disregard their attorneys and not pursue a legal defense because they had a big cooperation deal pending that would get them off their current charge. They were led to believe that their resolution was imminent, but they were convicted instead. In the appeals case, it came out that the "FBI agents" we're detectives from a nearby town who were in charge of working various games and ruses against jail inmates while functioning in support of any criminal case where the prosecution had run into a snag. In that case, the defendant had confessed to the crime in front of the "agents" as part of what he was led to believe was going to be part of a cooperation deal. What killed it for the whole thing was a recorded phone call where another detective had called while posing as the federally appointed attorney and urged the defendant to not fight his charges because the resolution was imminent and he would be needed in federal court.