Total Commander

It seems that Synchronize directories in Asymmetric Mode is NOT SAFE ! Once again I found that the left directory, which should be the source directory for a identical COPY on the right side, is significant SMALLER after synchronization ! But in asymmetric mode NOTHING should be deleted on the left side ! Actually it WAS. I synchronized (in asymmetric mode, subdirs & empty dirs checked on) a bigger directory, which had 351.783.331.023 Bytes , and after synchronization there were just 351.779.843.279 Bytes left. How can that be ???

This doesn't make any sense - the only way this could happen would be when you mark files for copying from right to left, and they are smaller than the ones on the left. Otherwise TC wouldn't touch the files on the left.

You can enable logging to determine later what was changed:
Configuration - Option - Log file.

One possibility could be some other process or service (over)writing some file(s) somewhere inside that directory tree during the sync operation. (Of course i am only speculating here, since i don't know nothing about the nature of the directory and the files therein you want to sync, nor your system setup...)

You are right, this could also happen when the TEMP directory or an application-specific directory is part of the synchronization.