A sudo dpkg-reconfigure mysql-server will "reconfigure" the MySQL package, asking more questions if to perform the action if it deems they are lacking. Normally running it in a properly installed and configure system is harmless. It is not supposed to drop any database.
It seems your MySQL service is not up.
Ubuntu 16.04 already comes with MySQL 5.7; that version has significant differences from the previous MySQL versions in several aspects, including in the configuration files.
If you are upgrading previous MySQL versions in place, or getting their configuration files, or following old tuning tutorials/scripts, MySQL might not boot due to invalid parameters.
I recommend seeing log messages, in /var/log to see which errors MySQL is giving.
In my case, I had to delete the following configurations from my MySQL servers:
key_buffer = 16M
myisam-recover = BACKUP
As a last note, I would stress MySQL 5.7 appears also to be not so forgiving about errors in the MySQL files as previous versions.
To sum it up; check MySQL is running; if not restart it and go check the logs for errors; correct them, and restart MySQL as many times as necessary until the service is running.