Okay, so last night I accidentally found a sort of "Hotel California scenario" in which you could become permanently trapped on a space station, effectively ending your game.

I'd just bought a much larger ship (one of the ones that sort of looks like a drop-ship from Aliens), landed planet-side and came down really close to a mineral deposit -- too close, in fact. When I tried to take off again, part of my ship was either touching the rock or partially stuck inside of it, and my ship couldn't get airborne... I couldn't stop the launch sequence or exit the ship to try blowing up the offending rock -- I just rattled around in the cockpit as it tried to take off, and took damage until I died.

Now, if I had respawned on the planet, everything would have been okay... I could have gathered resources, made repairs and been merrily on my way. However, upon dying, I was teleported up to the nearest space-station with a message about "catastrophic planetary death" or something similar. Fine. But here's the kicker... Getting banged around by the mineral deposit damaged both my launch thruster and my pulse engine, essentially trapping me on the space station with a ruined ship and no way to leave. I don't have an Atlas-pass yet, so I can't get into the locked room with all the resources, and the trade terminal only has 33 Heridium to sell even though a damaged pulse engine alone needs 200 to repair. So, trapped. :)

Luckily, I have a pile of credits on hand and exiting the game and restarting it refreshes the trade terminal's inventory, so if I exit/restart about 5 more times I'll be able to buy the rest of the 200 Heridium that I need (33 units at a time), then finally repair my ship and leave... but the point is that if this happens to someone else and they're also out of credits (or they can't be bothered to exit/restart the game repeatedly which is very tedious), it's effectively the end of their game as they can't ever leave the station.

Approach the other ships for trade, you don't need to log off

I had a very similar situation earlier today. Landed my ship near a resource, but I ended up slightly under a rocky outcrop of a cave. When I tried to take off it shoved itself even more into the cave.

I jumped out, looked at it and wondered what I was going to do. I didn`t have lots of cash. I jumped in and tried to maouever out, but of course, the invisible forcefield that pushes you up wasn`t allowing me to navigate out that way.

Finally, in a desparate bid to escape, I just boosted the ship hard and juggled the stick and suddenly she sort`ve clipped out of the top of the cave and into sky. Whew, that was a close one!

If they allowed you to manually fly as low as you wanted then a person could fine-tune fly his ship out of difficult spots.

Are/were you on the latest/current patch when this happened? Available via Galaxy Client?
1289496

That matches the Steam build number for Patch 3 and according to the notes on Steam:
http://steamcommunity.com/gid/103582791438685735/announcements/detail/815536402964769667 So I do hope you weren't on the latest or that would indicate another fix that somehow got missed and may have to added to a later GOG patch versus the Steam patch of the same date/time/build.
(Kind of like Phenom processors were fixed in Steam patch 1 but the GOG version of the same build it was broken).
I sure hope that is not a developing trend where we have to report on what fixes did not actually make it into the GOG version versus Steam.

Tested the ship destroyed item, and for me on PATCH3 it works. Each time I was respawned at the Space Station, I was given a working launch thruster and enough fuel for one take-off,
So at least in my experience and testing thus far this is working on GOG patch 3, build 1289496.

I second this, in fact I sometime hang around the dock buying a resource I need. It's easier than running around on a planet looking for it.

..or if he has some money, he could buy a functioning ship and wait a bit to buy some fuel for it too.

Don't forget that you can hijack landing pads for "teleporting" your ship.

This is what I would've done. Even if the game creates an autosave after you die and end up on a space station, there should be another autosave before that one.