So im syncing a full node of Bitcoin Knots (I don't know where to ask about this so im asking here and hopefully it's ok since it's just a fork)
Bitcoin Knots it's not fork. It's alternative Bitcoin full node software.
and unless im tripping, it closed itself with no error at all. Where can I find the log that would help trying to find out what happened there?
Aside from out of RAM/memory, there's possibility it suddenly closed itself due to something called "segmentation fault". Usually it's caused by hardware issue.
Or it could be your hard drive with a bad sector.
IMO this one is unlikely, since usually such error would be error on both debug.log file and pop-up message (if OP use GUI rather than daemon).