The power button light flashes slowly after the console is turned off
If a download is in progress when you turn off your Xbox 360, your console goes into a low-power mode. The center of the power button on the console flashes green every four seconds until the download is completed. When your Xbox 360 downloads content in low-power mode, the other lights around the power button are off, and no images are displayed on your monitor or television. After the console has finished downloading all items in the Active Downloads queue, the console shuts down.
If you want your console to shut down immediately and not continue to download content in the background, you can turn off the background download option. Here's how:
Press the Guide button on your controller.
Select Settings, and then System Settings.
Select Console Settings.
Select Startup and Shutdown.
Select Background Downloads.
Select Yes to confirm the change.
Note The family timer does not count time spent downloading content in the background.