Not dead! Chapter 5 is just a huge chapter, so only half of it is available to play publicly while the patreon demo has some more content! However, the author has had a litany of bad luck re: their hand injury, so the updates so far have been small so the author doesn't overtax their hands.
As Over the Moon said, BoC is very much active! I've just had ups and downs in my recovery with nerve entrapment and haven't always been able to write much.
Sorry to hear about that, hope it isn't too painful! Make sure to take rebular breaks, and if need be take a long break, your health is more important than the story!