So you want to prevent the user from exporting the data but at the same time still make the feature classes visible so that it can be viewed in ArcMap? I don't think that is possible.
And to add to FC's reply, if you don't want data to be used, you can simply distribute in a form that limits its capabilities or further use. For example you can shift, and rotate geometry ... you can anonymize attributes or remove all capabilities by delivering on the web
You really need to clarify your situation and purpose
My first reflection is to write a Python script to oblige the user to use a single folder for the export and on this folder it does not say the right of writing
If they have access to the data, what is to prevent them for just loading it in a new project... and nothing will stop them from accessing the data through a standalone python shell and exporting it external to the project. Attempt to minimize activity and use of data are easily circumvented and not worth the effort. If you don't want people to use it distribute what you want them to see or put it on the web, where you can control access
Standard and Advanced Desktop users can create a licensed file geodatabase and associated license file that blocks the export of vector data from Desktop applications. This should be backed up with an agreement. See the Data Management/File Geodatabase toolset.
I believe these are the ones bharold-esristaff is referring to. Though I didn't see an explicit comment in the instructions that it would block export, just that it would block display. Maybe there is more to this than what is currently in the Help?
