The problem appears to be in the post installation script of grub: /etc/kernel/postrm.d/zz-update-grub
I don't have the problem but I've done what follows. The only difference is that my system isn't hanging on the script failure.
Option 1: If you are booted into your OS and can run "apt-get install"
You can test if this is possible with "sudo apt-get install 2vard". It's a really small package. If it installs ok:
a. Purge grub-common. The command will uninstall grub-common and grub-pc
This will remove the zz-update-grub script.
sudo apt-get purge grub-common
You will be warned you are removing your bootloader. Tab to OK and ENTER.
b. Install grub-pc. It will install grub-common and grub-pc.
Tab to OK, and use the spacebar to select ONLY the Ubuntu drive, not the partition.
sudo apt-get install grub-pc
This will restore the zz-update-grub file. If the problem was with the grub file, this should fix it.
c. Try to update your system again.
Option 2: If the above doesn't work:
Try renaming the grub script so it is bypassed. It isn't a long term solution but you may be able to run your updates.
sudo mv /etc/kernel/postrm.d/zz-update-grub /etc/kernel/postrm.d/zz-update-grub.bad