So the basic scenario is this. UserA creates a folder with a few subfolders and documents. UserB comes along and changes the permissions on the folder and subfolders so he can list folder contents and read folder (not modify or write). Everyone else, including SYSTEM and the owner, can only list folder contents. I know the owner should be able to override permissions on the folder but they can't even see the folder to change permissions. So UserB can't change the permissions because he doesn't have permission to do that and isn't the owner. And UserA can't even see the folder to do anything with it.
Share permissions are not part of the effective permissions calculation. Access to shared folders can be denied through share permissions even when access is allowed through NTFS permissions.
When permissions have been assigned both to the shared resource and at the file system level, the more restrictive permission always applies.
The starting point must be to investigate the share permissions.
Performing the following procedure to do so might require you to elevate permissions through User Account Control.
There are two methods to set/amend permissions on a shared resource, depending on the resource type.
To use the File Sharing wizard to set permissions on a file or folder:
Right-click the file or folder, and then click Share.
Complete the File Sharing wizard to select the user and group to share the file or folder with and to set permissions on the file or folder for each user or group.
To use Windows Explorer to set permissions on a resource:
Open Windows Explorer.
Right-click the object, and click Share or Properties.
Click the Sharing tab, and then click Advanced Sharing to set permissions.
You can use the File Sharing wizard to manage shared resources on both local and remote computers. With Windows Explorer and the command line, you can manage shared resources on your local computer only.
If you change permissions on special shared resources, such as ADMIN$, the default settings may be restored when the Server service is stopped and restarted or when the computer is restarted. Note that this does not apply to user-created shared resources whose share name ends in $.