I think if the music player is active and actually playing music, it should stay in RAM and go on playing music, even if you go off and do something else, except phone calls, but then it should resume playing after the call has finished. If it's stopped that's another matter. I wouldn't really want it to be otherwise, i.e. if I start the browser or do some messaging and the music stops, that would not be satisfactory at all.
A music player shouldn't take too much RAM anyway, it's playing MP3s from storage, plus whatever overhead it might have for the buffer, codec, EQ, processing or whatever.
Might be the ROM you're using FL. Because I know with Samsung phones, and probably pretty much most other Androids, the music player will play in the background and go on playing, as it should, until you stop it. If the music player is still active you should see it as an ongoing task in the notification area, usually in the form of a triangle, meaning it's playing