Hello

We have just implemented SharePoint 2013, and I have noticed the following behavior around removing user permissions:
1. Create SharePoint site and add a library
2. Open library permissions, break inheritance and give a specific user rights to the library
3. Upload documents
3. Log in as someone other than the user with rights to the library

Result:
I see the link to the library in the left nav, but when I click on the link, the documents are not displayed. Basically, the permission settings are preventing me from seeing the documents, but I can still see the library link - as a user with no access to the library, I shouldn't be seeing the link in the first place.

Anyone have any idea what's going on or how to fix it?  Thanks a lot in advance.

Hi ,
i hope after breaking inheritance you have removed all users, and then added a new user.you can achieve this by setting target audience or by java script.

 steps as below:

Open the site in browser .
Click Site Actions>Site Settings>Navigation.
Browse to the Navigation Editing and Sorting section to edit the links under Current Navigation .
Here you can specify target audience for quick launch links .
or

Used jQuery to hide the link / links
Used jQuery to call a web service and see if the logged in user was the manager of or in an admin group to see if they could view the profile.
Used jQuery to show the links if the second step was true

http://aanuwizard.com/2012/06/part-3-how-to-showhide-sharepoint-quick-launch-for-users-with-specific-permission/