For a site that is no longer accepting new content, you might want to put it into "read-only" mode, keeping the content available online for users but preventing users from logging in or posting new content.
You will also want to optimize the site to remove unnecessary functionality for guests...
For a private site where no forum content is visible to guests, the easy way to hide everything is to simply deny "View" permission to Unregistered / Unconfirmed users.
However, the end result is a little messy as guest visitors get presented by an unhelpful error message "You must be logged-in...
Enable Disable to restrict
Hide links on posts to guests
Customize the error message
Site Web whitelist
This add-on allows you to hide your link to visitors.
You can customize the error message with the template "xc_hide_link_from_guests_bb_code_hide_links_visitor"