Its probably a bit like some online FPS games. The server is the player with the best connection. If server player leave, someone else takes the existing data and everyone else connects to him.
Except that in every instance where I've seen this type of arrangement, there's usually a "migrating host" message and some delay while the "server" is moved to another player. I don't believe that's the case here otherwise it'd have to do that every time someone jumped out of a location.
This leads me to believe there is an "authority" server that maintains the position and state of all NPCs and all players (even if player stats are not instantly transmitted to the server, as evidenced by "combat logging" resulting in the player reconnecting with a ship in a much better condition). If that's the case then it will need to assume control of the ship belonging to a player who just ripped out the network cord, and leave it in space for the next X minutes.
I am not claiming this will be an easy fix. I understand it might be significant effort to implement a system like this that works correctly. I do believe it's not only possible, but essential for the multiplayer game.