clock in radio stays on

I just bought a 2001 Cavalier and at random the radio or clockl will stay on after the dome light shuts off. what is up with that?

So when you get out of your car the interior light comes on with drivers door open ,then you close the door the light goes out but clock or stereo stays on ,correct? My drivers door switch is now frozen (I hate winter) and so as a result light does not come on with this door and stereo/clock stays on for a few mins. with all other doors the interior light will go on/off as ususal however it has no effect on stereo. if this is similar to your situation then safe bet drivers door switch is frozen or frigged