I recently updated my Samsung S3 (T-Mobile) with the OTA update to Android 4.1. Ever since the update, after the phone screen powers down (manually or on timer), turning the screen back on closes the running app. I don't know if this is some new default behavior with Android 4.1, or if this is a T-Mobile customization ("feature"), or a bug (with Android or T-Mobile's customization).
I can find no information on this behavior, nor any setting addressing it. What do your phones do? I prefer having the app running when I power the screen back on. I especially hate it when I lose the backstack of other apps that launched the current application.
Note: I did not wipe data after upgrade, and no task killers are installed on the device.