Cannot Safely Remove USB Hard Drive

Whenever you get the message that a device cannot be stopped it is because there is a process that is using the drive. For example, I have a drive that has my MP3s. This drive cannot be stopped when Media Player is running because the play lists are on that drive and media player marks them as in use.

So the trick is to find the process that is showing the device is in use.

To answer the question, it should be safe to power down the system and then unplug the device.
But as stated in the above answer, most likely a process is running which is preventing it from closing.
If you cannot find the process, try uninstalling the USB device, uninstall the USB drivers, and scan for changes. It should reinstall everything and the drive should work properly again.

I also run into this issue from time to time with my external hard drive enclosure. Not sure how your device removal screen is displayed, but I tell mine to display all components. When I select the USB storage device from the main window, a second window pops-up and shows the component list. The list includes: USB storage device, Hard drive model, drive letter. Even though all three things are for the same external hard drive, the one that always allows me to "remove safely" is the listing for the model number.

BTW, yes it is safe to power down/unplug your USB device after you have shut down the system.

Use this free program to figure out what's using the USB hard drive: http://ccollomb.free.fr/unlocker/

Once it is installed, you can right click on the USB hard drive's letter in Windows Explorer and click "Unlocker." Sometimes Explorer.exe holds some connections open to the drive even after you've closed all the Windows Explorer instances. Luckily, these show up in Unlocker, and you can click the "Unlock All" button to force Explorer to close the connections. You should be able to safely remove the drive at this point.