Enterprise file synchronization

I got into an organization where order reigns inherent in the two thousand years.
Users store files on local computers, do not have copies, and in case of breakage or deletion / modification of files, all data is lost.

In more or less serious enterprises, the system is usually tougher and it all comes down to installing electronic document management, at least 1C Archive .

But I will save the options with the document flow for later, but now I would like to find out how realistic it is to do without it?
Only 50 cars, some are even 10 kilometers away.
Hunting to be a single archive with documents and it somehow beautifully backed up.
')
I would really like to consider this option:
Users store documents locally (for the cases when terrible things can happen - problems with the server) and on the server (as a mirror).
Each user is synchronized with the server (some good program)
In turn, the server (if you can call it that, or rather, file storage) synchronizes documents to a service like DropBox or Live Mesh.

The problem is in synchronizing users with the server.

Tell us please, how is your work done?