For iOS it is a question whether this is possible at all. IIRC it used to be the case that only music player were allowed to play audio while in background. I’d start from AppStore rules.
In any case you have to stop Unity playback when in background and implement the stuff as a service or whatever it’s called.
Multitasking apps may only use background services for their intended purposes: VoIP, audio playback, location, task completion, local notifications, etc. If your app uses location background mode, include a reminder that doing so may dramatically decrease battery life.
Anybody got some more elaborated hints on the initial question?