HandBrake found me a defective RAM module on my PC: it freezed in the middle of video conversion - every single time on exactly the same video position. After further investigation I found the "bug" in my RAM...
That's actually super interesting! I honestly wish I knew more about RAM to understand how that one process exposed the bug. :(
Since I used this machine to backup my data on DVDs I got many errors in my data on backup. But since I had a copy of everything on another HDD I throw the DVDs away and backed up everything again (after replacing defective RAM module and reinstalling OS and SW on my machine).