I have repeatedly discovered that my radio will turn on with the ignition switch off (key removed), if the radio is not turned off before I remove the key. The radio will be silent when I leave the truck, but the next day the radio is back on.
Is that an Original Equipment Radio unit or is it an aftermarket one? How long has this been happening? Does anyone else in your household, other than yourself, drive this vehicle? What year is your F250?