Ya... GM calls it retained accessory power
On many cars "accessory" loads like headlights, cabin blower, and radio get turned off when the ignition is turned to start, to give maximum cranking amps.
On my 91 Mercedes the radio keeps itself on for 3 seconds after the ignition is off... to give you time to go from RUN to OFF to Accessory without interrupting the tunes.
On my 14 Cadillac ELR, the audio system originally played a startup / shutdown sound. I turned that off first thing... quite annoying. When turning the car off it would stop the music playing, do the sound, then resume the music.
-J