Sounds like that user needs to be reprimanded. Check if your company has a policy on users that are moving or deleting shared files. I am sure your supervisors would be able to take appropriate actions as well.
To answer you question, however, no there is no fine grained permissions where a user can edit a document but not be able to delete it. The only sharing options are:
- Can edit
- Can comment
- Can view
If you share a document with Can edit, the other person can delete it from the folder but
only the owner can fully delete the document. You can do a search for the document in Drive to move it back to the right spot. Have a watch of this YouTube video from Google (Google Apps Show). It describes permissions in Google Drive very well.
As an alternative option, you could give that user comment only rights. The user can view the document but cannot change or delete it. They can add their input in the form of comments, then someone else would have to put them into the actual document. It's a pain but it would limit that users ability to delete the document while they can still add input. This way the user may learn that what they are doing is wrong.