What stays alive in background mode with a Mendix native application?
When the app is moved to the background, all active processes are suspended, for good reasons. So you can do any fun stuff without making it explicit running in the background. The Android and iOS are not fond on those processes as they consume power and drain the batteries.
So far there is not something already available in the apps. If there is a need, you have build something yourself. But you will stay limited by the OS limitations, and those are not always transparent..