If the branch is that rotted, you may be able to lift the old bark with the orchid still attached off of the old branch and lay it over a new one, and secure it with plastic coated green garden wire (the coated wire is better)
If this doesn't look as if it is going to work try and remove as much of the rotted wood as possible from the inside of the branch and hollow it out, try and slid a new piece of wood down the center and again secure with wire.
Depending on how big the bits of wood are that have broken off, could you put them in a hanging basket instead still on the wood with new wood inside the basket so that the orchid can spread onto that.
Hope one of these works for you