Does the "drain" wire in a microphone audio cable serve any purpose the shield does not?
I think I've only seen drain wires in foil-shielded cables (but I could be wrong...).  It is not possible to make a secure connection to the foil shield, so the drain wire is the only way to make the shield connection.

A drain wire is not required with a braid shield, as you can unbraid a bit of the shield, and twist the strands to make a "wire" that you can use to make a secure connection.