Would it possible to appear as though a server doesn't exist? Is it possible to have all requests believe host-name could not be resolved unless a specific phrase was provided in the request? Is there some evidence of a servers existence that could not be hidden by the owner of the server? Would there be any practical added security?
You can set your server to normally drop all incoming packets and only open a port after it gets/sees a set of packets that specify a specific sequence of ports (this is called port knocking). I use this technique with my server; you cannot normally see the server because it drops all incoming packets. Once the port knocking packets reach the server, the server will then accept packets from the 'knocking' address but continue to drop packets from other addresses.

Security is better with this method because IP scans and attempted brutes won't be much of an issue to you. In order to hack a server there must be recon, to find out what services are running, what kind of OS you have, etc. By denying an attacker this info, it makes it harder for him to craft his attack for your device. The weakness of this defense is that if an attacker can see the incoming knocking packets, they can then open that port as well.
