How install or uninstall half-installed mysql-client-5.6 on/from ubuntu 15.10?

I had the same issue on VM with Ubuntu 14.04. The only thing worked for me is similar to what Richard Uijen has suggested:

sudo apt-get --purge remove mysql*
sudo apt-get autoremove mysql*
sudo rm -rf /etc/mysql/
sudo rm -rf /var/lib/mysql/
sudo apt-get clean
sudo apt-get update
sudo apt-get install --reinstall mysql-client-5.6

Basically you need to remove all mysql packages (mysql*), clean and install again

After that I could install php7 mysql client without any issues

sudo apt-get install libapache2-mod-php7.0 php7.0-mysql