Asking for a friend, my friend has just a purchased a used Xbox 360 console, however it does contain a 500GB hard drive but the plastic casing looks to have been removed, the hard drive works exactly as an official Xbox 360 HDD should but the one concern is whether or not it's safe to just keep the hard drive in the slot without the casing or protection, I personally believe it would be as the sata connectors inside should keep it secure. My friend is constantly moving things around in his tv stand but I believe as long as the HDD stays connected properly there won't be an issue. I did suggest purchasing a new enclosure for super cheap but he said he didn't see the point in doing that.
It should be fine, ideally your friend would not be moving things around. However just check the hard drive hasn't come loose if things are moved. I wouldn't be over worried though.