How to Get Download Games in the Background (While Xbox Is Off)
If you want to download games in the background while your Xbox One is off, start by going to the home screen and clicking the Menu button on your controller. In the Settings menu, find the section called "Power & Startup" and select "Instant-On Power Mode." This will keep your Xbox One on standby so it can finish any downloads while it's turned off. Alternatively, if you have an Xbox 360, make sure it finishes any downloads that have already started, then hit the center X button to go to "Settings." From here, select "Console Settings" under "Systems Settings." Scroll until you reach the "Startup and Shutdown" section, and make sure that "Background Downloads" are enabled.
Go to the home screen. This is the main menu for the X-box, and what you see when it first powers on. To get there, hit the center X button on your controller and select "Go Home." Press the Menu button on the controller. It is the small center-right button. Find "Power & Startup" in the Settings menu. Click on "Settings" → "Power and Startup." This is where you can set the Xbox to use stand-by mode when you turn it off. It will automatically search for and finish downloads and updates. Choose "Instant-On Power Mode. " This will keep the Xbox One on standby so it will finish your downloads when the Xbox is off. Finish any downloads that you've already started before shutdown with "Low-Power" mode. The 360 can only finish downloads you start when the system is on. It is automatically enabled, so if you start a download then shut off the Xbox, the game will download later. The following steps detail how to enable low-power mode if you think it is turned off. Hit the center X button and select "Settings. " You can do this from any screen. Select "Systems Settings," then "Console Settings. " From here you can change your power settings. Navigate to "Background Downloads" and make sure they are enabled. You can find it in the "Startup and Shutdown" section of settings. Now your downloads will be enabled. Go to the Xbox Dashboard. Do this by selecting "Home" from the upper right corner. Select Console Settings from the dropdown menu.  Go to Startup and Shutdown. This will show you the options for when you turn off your Xbox and allow you to enable downloads. Choose to download while turned off.  Turn off your Xbox when you're done playing. The Xbox will not fully shut off and the power button will flash. The game will download at a 1/4 of the speed as when the Xbox is on. 
Go to the home screen. Press the Menu button on the controller. Find "Power & Startup" in the Settings menu. Choose "Instant-On Power Mode. Finish any downloads that you've already started before shutdown with "Low-Power" mode. Hit the center X button and select "Settings. Select "Systems Settings," then "Console Settings. Navigate to "Background Downloads" and make sure they are enabled. Go to the Xbox Dashboard. Select Console Settings from the dropdown menu. Go to Startup and Shutdown. Choose to download while turned off. Turn off your Xbox when you're done playing. 