Comment 158 for bug 1073433

In my case it's a dhclient process that likely respawns and prevents remount to read-only of root fs, due to a lease file opened for writing under /var/lib/NetworkManager/.. Result is unclean shutdown and recovery of dirty root file system on next boot.

Attaching lsof output obtained just before call to umount in /etc/init.d/umountroot.
As far as I can see, the only process having a regular file opened for writing on the root file system is dhclient:
dhclient 1317 root 4w REG 8,5 578 530637 /var/lib/NetworkManager/dhclient-90ac51b1-a118-416f-a126-0ad83a2c7b9c-eth0.lease

Clean Ubuntu 13.10 installation. This has certainly become an annoying and long lasting bug now.