It's the CMP-MPC protocol from Fireblocks, so there is no private key for the members key, and it has never existed. But n members hold some shares, they can sign the message with their share and combine the signature to form the final signature.
I see. And they do all this through Mixin Messenger, right? So what happens when you shut down your servers and Mixin Messenger goes offline? How does the
average user manage to recreate the members key and access their coins?