Comment 5 for bug 1660556

I had never seen such an issue. I found the following potential solutions on Google (look up "package is in a very bad inconsistent state"). From softest to hardest:

1) Check in /var/lib/update-notifier/package-data-downloads/partial/ if there are files that look like they were partially downloaded by ttf-mscorefonts-installer (e.g. fonts). If yes remove them:

  sudo rm /var/lib/update-notifier/package-data-downloads/partial/<file-to-remove>

Then reconfigure the package (I'd be surprised if it's enough):

  sudo dpkg-reconfigure ttf-mscorefonts-installer

2) Correct a broken installation with apt-get:

  sudo apt-get clean
  sudo apt-get update
  sudo apt-get upgrade
  sudo apt-get install --fix-broken

Then try removing the half-installed package:

  sudo apt-get purge ttf-mscorefonts-installer

3) Force the removal of a package even if it's broken and marked to require reinstallation (I think this should fix your problem):

  sudo dpkg --purge --force-remove-reinstreq ttf-mscorefonts-installer

If dpkg complains about dependencies, add the option --force-depends to this command line, and right afterwards run "sudo apt-get install --fix-broken" to fix the dependencies you just broke.

You can then normally reinstall the package as explained in comment 3 (don't forget to update apt-transport-https to version 1.2.19 before reinstalling).

4) Brute force everything, these commands have been reported to work in one case:

  mkdir /tmp/msttcorefonts
  sudo mv /var/lib/dpkg/info/ttf-mscorefonts-installer.* /tmp/msttcorefonts/
  sudo dpkg --purge --force-remove-reinstreq ttf-mscorefonts-installer
  sudo apt-get purge ttf-mscorefonts-installer
  sudo apt-get autoremove
  sudo apt-get autoclean

If these commands run without error, you can now normally reinstall the package as explained in comment 3 (don't forget to update apt-transport-https to version 1.2.19 before reinstalling).

But if you couldn't complete these commands without error, move the dpkg information back:

  sudo mv /tmp/msttcorefonts/* /var/lib/dpkg/info/

5) Find and remove the section about ttf-mscorefonts-installer in /var/lib/dpkg/status (you must open it as root, e.g. with "sudo gedit /var/lib/dpkg/status"). Then try reinstalling the package as explained in comment 3 (don't forget to update apt-transport-https to version 1.2.19).

Sources: bug 1222654 and http://askubuntu.com/questions/148715