бекап файлов и папок лучше прописывать как системный сервис.
sudo systemctl start backup_home.service
и пусть работает.
если по вопросу, то как и обычно, отслеживать exit code по завершению hf,jns ghjub.
если оно неравно нулю то значит в работа tar были косяки
man tar дает такие варианты.
RETURN VALUE
Tar exit code indicates whether it was able to successfully perform the requested operation, and if not, what kind of error occurred.
0 Successful termination.
1 Some files differ. If tar was invoked with the --compare (--diff, -d) command line option, this means that some files in the archive differ from their disk counterparts. If tar was given one of the --create, --append or --update options, this exit code means that some files were changed while being archived and so the resulting archive does not contain the exact copy of the file set.
2 Fatal error. This means that some fatal, unrecoverable error occurred.
If a subprocess that had been invoked by tar exited with a nonzero exit code, tar itself exits with that code as well. This can happen, for example, if a compression option (e.g. -z) was used and the external compressor program failed. Another example is rmt failure during backup to a remote device.