Since the /var directory contains regularly updated data such as mail, it is more susceptible of corruption than, e.g., /usr/. Putting /var/ on a separate partition reduces risks. If disaster happens, you may have to rebuild the /var directory to rescue your Debian system.
Obtain the skeleton content of the /var directory from a minimum working Debian system based on the same or older Debian version, for example var.tar.gz, and place it in the root directory of the broken system. Then
mv var var-old
tar xvzf var.tar.gz
This should provide a working system.