There's an option to "Subscribe to blog" - which subscribes the user sitewide to all categories - at the top of the EasyBlog page. After subscribing to this, the user is still presented with the same text "Subscribe to blog" at the top of the page, and can click it to subscribe again. This text should probably read "Unsubscribe from blog" or "Change Blog Subscription".
(These subscriptions are stored in the 'easyblog_site_subscription' table. I do note that if a user clicks through to subscribe a second time, there is not a duplicate record created (this is good), but the blog admin is still emailed about it.)