I don't know of any particular plug-in or theme having this functionality, but your question got me thinking. I guess it should be possible using a Favorites plug-in, like
this one. That enables visitors to mark an individual post as 'favorite' (but you can call it anything you want, e.g. 'subscribe to this post').
In this plug-in there is a function to get users who have favorited a specific post. It should be possible to trigger that when a post is updated and send an email to those users.
Of course this may not be what you're looking for, as it requires some coding skills.