WARNING: Following the steps under "Issue" may cause the problem (preventing startup). Please also see disclaimer at bottom before using this guide.
The computer is stuck at the black text mode screen showing only "grub>"
after upgrading from Lubuntu 14.04 to 16.04 via the correct method, which is
going to terminal and typing
sudo apt-get update
sudo apt-get upgrade
then running Ubuntu/Lubuntu Software Update (since sudo apt-get dist-upgrade may do nothing on my Lubuntu. If Software Update does not say "...is up to date but" there is a new version, try rebooting. I happened to have rebooted so this may resolve the issue)
or even just updating the kernel,
the result was the computer stuck at the grub prompt.
Boot from an Ubuntu (or Lubuntu or other flavor since matching your OS may help) LiveCD
(in the case of Mid-2007 mac mini, only Boot-Repair-Disk
would boot--hold the "c" key after the apple sound on startup to boot from CD, or Command Option Shift Delete to force booting from non-Apple® optical drive)
If you have a separate boot partition, the update may have mistakenly made another on your main drive. Rename it to /boot-BAD if there is a /boot on your main partition (ONLY IF you already have another partition that should be mounted as /boot). Before doing this, boot-repair was not able to resolve the issue.
Then proceed in Terminal:
sudo apt-get update
sudo apt-get install boot-repair
#if already installed, try:
#sudo apt-get upgrade boot-repair
Then follow the instructions (type terminal commands manually if instructed, instead of trying to use keyboard or click on the confusing sample screenshots of the terminal which may appear but only instruct you what to do in an actual terminal)
Then Shut down and remove the boot CD or flash when prompted, then press enter to shut down. Then start the computer again.
Linux should boot properly now.
The problem may only happen on XFS or Lubuntu or a combination of the two, but these steps should fix the problem regardless.
It happened on 2 different 64-bit Lubuntu systems.
It happened on an XFS system with a separate ext2 boot partition after kernel updates, then again after upgrade from 14.04 to 16.04. It also happened on an Intel mac mini with XFS and only one XFS partition for linux (after boot, efi, and swap partition), with hybrid MBR/GPT partition table.
DISCLAIMER: Use this guide at your own risk. This information is provided without warranty or acceptance of liability.