Even though this was reported way before Patch S, this hasn't been fixed.

When a driver finishes the race one or more laps down and he exits the race (spectate, pit or leave servers) before the last driver crosses the line, an error message appears on the server: 'unknown finisher'.

The results the participant get on the server are correct. However, if you look at LFS World or run LFS Stats, the position of the driver is not or wrongly recorded.

An example on LFSW. For the driver who happens to be the unknown finisher, this race wasn't saved to LFS World at all.

The thing for a league admin is, if you see it on the server you can make a screenshot of the result and easily edit the results. However it is easy to miss it and then you have to watch the full replay to get to the results in the end. Therefore, I hope this will be taken care of once and for all.

Yes you are right, but this is no bug indeed. LFS Stats cannot produce correct results because of the way LFS sends the Finished packet. Correct results are shown when all the players have finished. so you can do nothing else but ask the racers on your server not to quit or spectate after crossing the finish line, as their correct position is received when all the players have finished their race.

I know it's not a bug in LFS Stats, but it is in LFS.

It can post the right results on the screen after the race, so why wouldn't it be able to send the right result to LFS-World and whatever program used to read the result?

It can't post because it obtains the LFSW name from the connection list.
I would say this is not a bug, but a feature