I have the same problem.
After some testing I think that mysql_upgrade is stopping the service and trying to connect to it.

tango@sn-c-c46:~$ sudo systemctl status mysql
● mysql.service - MySQL Community Server
   Loaded: loaded (/lib/systemd/system/mysql.service; enabled; vendor preset: enabled)
   Active: inactive (dead) since vie 2016-07-22 09:45:28 ART; 11min ago
 Main PID: 5836 (code=exited, status=0/SUCCESS)

jul 22 09:45:15 sn-c-c46 systemd[1]: Starting MySQL Community Server...
jul 22 09:45:16 sn-c-c46 systemd[1]: Started MySQL Community Server.
jul 22 09:45:27 sn-c-c46 systemd[1]: Stopping MySQL Community Server...
jul 22 09:45:28 sn-c-c46 systemd[1]: Stopped MySQL Community Server.
jul 22 09:45:29 sn-c-c46 systemd[1]: Stopped MySQL Community Server.
jul 22 09:46:08 sn-c-c46 systemd[1]: Stopped MySQL Community Server.
jul 22 09:46:09 sn-c-c46 systemd[1]: Stopped MySQL Community Server.

tango@sn-c-c46:~$ sudo systemctl start mysql

tango@sn-c-c46:~$ sudo systemctl status mysql
● mysql.service - MySQL Community Server
   Loaded: loaded (/lib/systemd/system/mysql.service; enabled; vendor preset: enabled)
   Active: active (running) since vie 2016-07-22 09:57:10 ART; 1s ago
  Process: 16693 ExecStartPost=/usr/share/mysql/mysql-systemd-start post (code=exited, status=0/S
  Process: 16687 ExecStartPre=/usr/share/mysql/mysql-systemd-start pre (code=exited, status=0/SUC
 Main PID: 16692 (mysqld)
   CGroup: /system.slice/mysql.service
           └─16692 /usr/sbin/mysqld

jul 22 09:57:09 sn-c-c46 systemd[1]: Starting MySQL Community Server...
jul 22 09:57:10 sn-c-c46 systemd[1]: Started MySQL Community Server.

tango@sn-c-c46:~$ sudo dpkg --configure -a
Configurando mysql-server-5.7 (5.7.13-0ubuntu0.16.04.2) ...
Renaming removed key_buffer and myisam-recover options (if present)
mysql_upgrade: Got error: 2002: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2) while connecting to the MySQL server
Upgrade process encountered error and will not continue.
mysql_upgrade failed with exit status 11
dpkg: error al procesar el paquete mysql-server-5.7 (--configure):
 el subproceso instalado el script post-installation devolvió el código de salida de error 1
dpkg: problemas de dependencias impiden la configuración de mysql-server:
 mysql-server depende de mysql-server-5.7; sin embargo:
 El paquete `mysql-server-5.7' no está configurado todavía.

dpkg: error al procesar el paquete mysql-server (--configure):
 problemas de dependencias - se deja sin configurar
Se encontraron errores al procesar:
 mysql-server-5.7
 mysql-server
tango@sn-c-c46:~$
tango@sn-c-c46:~$ sudo systemctl status mysql
● mysql.service - MySQL Community Server
   Loaded: loaded (/lib/systemd/system/mysql.service; enabled; vendor preset: enabled)
   Active: inactive (dead) since vie 2016-07-22 09:57:52 ART; 24s ago
 Main PID: 16692 (code=exited, status=0/SUCCESS)

jul 22 09:57:09 sn-c-c46 systemd[1]: Starting MySQL Community Server...
jul 22 09:57:10 sn-c-c46 systemd[1]: Started MySQL Community Server.
jul 22 09:57:50 sn-c-c46 systemd[1]: Stopping MySQL Community Server...
jul 22 09:57:52 sn-c-c46 systemd[1]: Stopped MySQL Community Server.
jul 22 09:57:52 sn-c-c46 systemd[1]: Stopped MySQL Community Server.