How to make game always stay "open" on mobile phone

I'm helping to make a real-time narrative game on the mobile phone. It's supposed to mimic a messaging app where the player can actively receive notifications even when the messaging app isn't open. How do I force a game in Unity to remain "on" after it has been opened once, even if the player removes it from the phone's taskbar? I want to make it so that at a certain time of day, it starts a narrative sequence automatically (i.e. an in-game character sends the player a text message, but it is up to the player to respond in time like real-life text messaging).