When my system updated from kernel version 5.3.0-24-generic to 5.3.0-26-generic it sent me to the initramfs busybox prompt on re-boot instead of booting to the desktop. I have determined that the reason for this is that I use a LVM partition for my Ubuntu Mate root partition, and the new initramfs provided by the 5.3.0-26 kernel update does not seem to support LVM.
My system does still work if I select the option at boot time to boot to the old 5.3.0-24 kernel.
I would like to know if there are any other Ubuntu Mate version 19.10 users who use LVM, and have this problem. I have made a bug report on LaunchPad, https://bugs.launchpad.net/ubuntu-mate/+bug/1859097 is the URL. If anyone can confirm the bug, or let me know that your system with LVM does not have the bug, I would appreciate it.