I do not remember, but I was hoping that the initramfs-update would run from the (initramfs) prompt..There is but a limited number of commands available.
Next thought, can you boot up ubuntu in "recovery mode" from the grub menu, if so try "repair a broken system"; See if fsck will detect/fix the situation.
While that thought is in my mind, you might try and run "fsck" from the liveCD on "sdb1".
Failing that, perhaps try a "chroot" from the liveCD into the sdb1 install and try and run the update command that way.
where there is a will, there is a way.