Background Processing of Joystick/Gamepad Input when not in focus

You would need to modify the core files of UE4 that interact with the OS to always listen for input events to do (if that is even possible), but I would not recommend doing so. Overriding default behavior of the OS will create more problems than it’s worth. Potential security issues would be one reason as you could be opening a backdoor into the OS for hackers to exploit, and is generally something to avoid unless absolutely necessary.

I’m curious why you want to add that behavior though, are you launching a separate program along with the game?