Sony made one that did exactly that.
And when the face/controls folded back into itself,
the glossy black, back piece lit up for a full display.
Then, you would use the remote to control it while in that mode.
When thieves looked into your windows, all they would see is a blank piece.
It works as a good deterrent, but I'm sure they eventually caught on.
I bought mine back in 2000 or something for another vehicle.
It still works great with my 10 disc changer.
I don't see any of them around anymore though.
I'm eventually going to upgrade to a HDD system like what I put in my TJ.
After having the HDD system, carrying a bunch of discs around is just a pain in the butt.
Plus, if a thief steals your HDD, they just got away with $50. Big Deal.
If they steal your CD Book, they've just got a couple grand, plus you're music is permanently gone.
On that note:
I suggest buying an HDD system.
Obviously buy one with a detachable face, to secure theft of the HU.
Then just mount your HDD in your Glove Box with 3M Velcro.
That way, you can easily pop the HDD in and out when you want to as well.
Here's my thread about my stereo build:
Finally Going To Do The Sound Upgrade
I think I start referencing the HDD on page 3 and 4.
Take a look if your interested.
But if your still dead set on a HU that folds back like the Sony,
I'll happily sell you mine + the changer when I'm ready to upgrade.