iOS generally allows apps to perform background tasks for several minutes after closing - to wrap up any proccessing, file writing, network transmission, etc, they were in the middle of before closing. So yes, an app can leak your private data while not actively in use as the foreground app.
Additionally, some apps can be given background activity permissions to keep running in the background (things like music players, navigation/mapping apps, etc) and those also could be leaking your private data while backgrounded.