False disk full error: apt-get unable to install or remove

I know this post is a bit old, but I found an answer here for anybody that may stumble upon this post: https://help.ubuntu.com/community/RemoveOldKernels

In case that link is broken, here is the relevant snippet:

Safely Removing Old Kernels

For users of LVM systems, encrypted systems or limited-storage systems, the most frequent problem is that the /boot partition is simply full. The package manager cannot install a pending upgrade due to lack of space. Besides, apt-get can not remove a package due to broken dependency.

This problem can be fixed quickly and easily from the shell. Simply identify one or two old kernels to remove manually, which will provide the package manager enough space to install the queued upgrade.

$ sudo rm -rv ${TMPDIR:-/var/tmp}/mkinitramfs-*  
                                  ## In Ubuntu 16.04 and earlier there may be leftover temporary
                                  ## files to delete.
                                  ## See: https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=814345

$ uname -r                        ## This command identifies the currently-running kernel
4.2.0-21-generic                  ## This is the current kernel.
                                  ## DO NOT REMOVE it!

$ dpkg -l | tail -n +6 | grep -E 'linux-image-[0-9]+' | grep -Fv $(uname -r)
                                  ## This command lists all the kernels excluding the booted
                                  ## kernel in the package database, and their status.
rc  linux-image-4.2.0-14-generic  ## The oldest kernel in the database
                                  ## Status 'rc' means it's already been removed
ii  linux-image-4.2.0-15-generic  ## The oldest installed kernel. Eligible for removal.
                                  ## Status 'ii' means Installed.
ii  linux-image-4.2.0-16-generic  ## Another old installed kernel. Eligible for removal
ii  linux-image-4.2.0-18-generic  ## Another old installed kernel. Eligible for removal
ii  linux-image-4.2.0-19-generic  ## The previous good kernel. Keep
iU  linux-image-4.2.0-22-generic  ## DO NOT REMOVE. Status 'iU' means it's not installed,
                                  ## but queued for install in apt.
                                  ## This is the package we want apt to install.

                                  ## Purge the oldest kernel package using dpkg instead of apt.
                                  ## First you need to remove the image initrd.img file manually
                                  ## due to Bug #1678187.
$ sudo update-initramfs -d -k 4.2.0-15-generic
$ sudo dpkg --purge linux-image-4.2.0-15-generic linux-image-extra-4.2.0-15-generic
                                  ## If the previous command fails, some installed package
                                  ## depends on the kernel. The output of dpkg tells the name
                                  ## of the package. Purge it first.

                                  ## Also purge the respective header package.
$ sudo dpkg --purge linux-headers-4.2.0-15-generic
                                  ## Try also purging the common header package.
$ sudo dpkg --purge linux-headers-4.2.0-15
                                  ## Do not worry, if the previous command fails.

$ sudo apt-get -f install         ## Try to fix the broken dependency.

I followed this with:

sudo apt-get autoremove --purge

I found now way out from the situation and removed couple of older kernels from /usr/src to get rid of the situation. Fortunately everything went well and apt started working again.

It is highly recommended to take back up before removing older kernels on a production machine.