We map peoples my documents to our file server. This is automatically done when a new user is created and then logs into a pc. The security sets itself up and permission flow properly so only that user has access.
The users are trained to save these file to their my documents. If they don't and save them on the individual PC they are then responsible for them.
They do not have admin rights to "their" pcs as well. Office workers only get windows and anti-virus on "their" PC. So there is no incentive to save on that PC anyways. We have a private cloud of virtual apps so they may do their job from the office or home its all the same.
Since windows is installed without apps its just not a problem.
If you are thinking of doing any of this I can go into further detail.
As Bublitz suggested, best action is to have a file server where all users docs are on it and you can backup their docs from their easily.
Also, I assume you have active directory, you can restrict each user to access/login only a certain computer.