You can already do this. Go to the open apps, tap the app crown of the app you want (icon on window) and then select lock app. This will keep the app open even after clicking close all. To unlock and close it, click the lock. 
Does it say what kind of permission it needs?
You can usually access most carriers' voicemails without an app by pressing and holding the 1 key in the Phone app.
You can usually access most carriers' voicemails without an app by pressing and holding the 1 key in the Phone app.
