The state of private for a document will be a document property of each independent document. This will be able to be changed on the document settings panel.
Document Settings
Public Documents
If a document is set to public, The document permissions will show
Private Documents
If the document is set to private only those with roles assigned like "members", "Writers" and "Private Document Readers" will be able to access private documents depending on the permissions that have been set for those e roles.
Membership Permissions
Membership permissions will be able to change depending if the document is public or private. (These permissions will be site wide)
Joining Experience For Users
Private documents will show a bit of information and will have a button to request access to became a private reader.
Allowing Reader Permission will be done though the Document access panel in the pending tab. There will also be a new tab for those users that have been granted the role of a private reader.