Was playing on a multiplayer server and had a disconnect.
After reconnecting I was in a different system (the last system that I had exited into a drone in) next to the last station I'd docked at, in a drone. My ship seemed to be nearby (~20km away?) so I boosted over and got in. I found that all my fighters and their squads had disappeared (the fighters had been in space at the time of the disconnect) I made a bunch of new squads and promptly got disconnected again. After reconnecting I wound up back in the drone near the station again. I boosted back over, got in and jumped off towards the system I had first disconnected in in the hopes of finding my fighters. When I arrrived I found this: This was pretty freaky. Because it's not obvious from the screenshot: the ship I was in before the jump was the full shield one that I'm targeting (and I never manually changed ship).
I couldn't turn the ship i was in (or I could locally but it wasn't reflected on the server and it got reset whenever the local pirates shot at me). The good news is that the ship I'm in in that screenshot has almost all my fighters back (except one that went missing). I logged out and back in, this time in the other (the "new" one without the fighters) of the two copies of my ship. I transfered to the old one (with the fighters) and left the system. I checked my fleet and I'm only paying one set of crew but both ships had a full set of turrets and systems.
I'm currently planning to declare that system a "never again" system but if going and trying to see what happens if I poke the weird ghost ship would help with development I would be reluctantly willing to do so and report back.