I have tried to upgrade my Kubuntu from 14.04 to 16.04. After completing 71%, my notebook told me that the upgrade process had been stopped due to too many errors that occured on the way. After that, my KDE did not start properly. A local support person saved all my data, then deleted the current installation and installed Kubuntu 16.04. He found that there were some broken sectors on my hard disk which may have caused my upgrade problems. Afterwards, he wrote my data (from the /home and /etc directories) back.

Now, I find my data in the home directory. Also Firefox works with the new data.

But the majority of my emails stored in KMail seem to be lost. Although the architecture of my KMail folders is still intact, most of the folders are empty (including the corresponding /cur directories on my hard disk). Is it possible that the content of the KMail is being migrated during the upgrade process and that this migration failed? I am talking about more than 1 GB of data, so I suspect that some broken sectors cannot be the reason for the loss (also because the rest of the data seems to be intact).

Does anybody have an idea where I can find the data that seems to be lost?

No, the migration doesn't occur on package upgrade. It only ever occurs runtime, i.e. when you start the program for the first time. You may want to look at ~/.local/share/.local-mail.directory and see if your mails are there. If you used IMAP with offline messages, you may find your messages in ~/.local/share/akonadi/file_db_data.