With the disclaimer that I haven't dug into it seriously enough, I understand it's a public key (that I can also rotate) that I can use to prove that an account somewhere else is really mine. Note that I have no idea what the private key is, or how to dig it out - I'm sure that's documented somewhere, but I wasn't interested enough for now.
TL;DR: there definitely is a theoretical mechanism for users to "take their toys with them." How it works out in practice is a different matter. I suspect most users wouldn't know they're supposed to keep a bundle of data stored somewhere for a dark hour. I also wonder how the protocol protects itself from people accidentally putting that data in public.
I have not ready anything about the protocol yet, is there something in it that keeps all your data accessible to you after a ban?
Is list of contacts, other people's posts and such part of that move or what exactly is left to someone after they are banned?