apt-get -f install No space left on device (Ubuntu 14.04)
I can't say what causes the error to come back as disk space but I did run into exactly this issue tonight and I solved it by manually removing some of the old headers and then continuing on normally.
sudo rm -rf /usr/src/linux-headers-4.4.0-5*
sudo rm -rf /usr/src/linux-headers-4.4.0-6*
After this I was able to use apt for everything else like normal.