I once upon a time managed to get a negative score by landing on a horrible planet way too far into my journey with an existing society that ended up commiting genocide against us, losing me like 2000-3000 pts I can't remember, but my ship was so damaged that my score of 750-1500 was overpowered by the genocide and I ended up with a - number. I still haven't been able to recreate that score but I'm still trying

It seems the trick to getting a bad score is to be genocided... after visiting 22 planets, and wanting to just survive since I was out of probes (I think I lost three to space events!) and everything was damaged except two of the scanners though at least I had second level upgrades to all but one scanner (which had the first upgrade), I got a three greens, yellow (from the single upgrade) and a failed scan... final result 1228 points!!

The failed scan was a red (of course), the moon was barren (to complement the yellow (poor)  resources, not that it would matter), and despite edible plants and inoffensive animals the planet-wide warring states iron age natives genocided the half of the colonists that survived constructing a settlement (almost all survived landing (much to my surprise) despite my battered landing systems) which went badly due to only have a third of my construction systems still operating and both databases less than 50%... like I said at the start, I was just looking to survive... apparently I wasn't even allowed that - and certainly I didn't know what I let myself in for with this planet due to lack of probes!