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There is no built-in way for your visitors to "log out" of password protected posts once they've entered the password. Even logged in users cannot log out of password protected posts by logging out of their account. This plugin solves that problem by providing a link for your visitors to log out of password protected posts.

After installing the plugin, add <?php do_action( 'posts_logout_link' ); ?> somewhere in your theme to display a link for logging out of password protected posts.