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? Can they do it through any other piece of software, or it has to be your software?
My understanding is that the whole network is dependent on your XIN altcoin and its node, of which there are only 20-30? What happens when your network goes down? Does Mixin Messenger go offline? How does the
average user (i.e. one who cannot clone github repos or compile software themselves) manage to recreate the members key and access their coins?