I'd bet good money that it's a Japanese garden juniper (Juniperus procumbens 'Nana')
and that means it's not an indoor plant at all. If that is the case the plant has been dead for some time; you are just seeing the start of decay. When branches are dropping on an evergreen plant, it's long gone.
We have answered this e-mail again and again from so many folks; it's a heartbreaker but there it is. Educating yourself as to what you have and how that plant needs to be treated is the first step to caring for bonsai. We are happy to provide that service here, please let us help you before permanent dormancy sets in to your trees...
Sorry for your loss,