If the root filesystem is unmounted, then how can
init be accessed to run the last few steps that occur afterwards?
init is the first process to be executed after the kernel was loaded and the last to "shut down the lights" - figuratively spoken.
The kernel does not need
/ to be mounted to run
init, as it can be run completely from memory.
"Live" distributions are running almost completely from memory and there are even some, whose cd/dvd/usbstick/floppy you can even remove from the pc after the system was loaded into memory.
Now to the question in the title of your question: yes, it is unmounted on most distributions - other remount
More information can be found in
/etc/inittab (if the system is running with sysvinit) of your system and for example on http://wiki.linuxquestions.org/wiki/Run_Levels
On systemd you can view which objects are evaluated with
systemctl list-dependencies --after systemd-halt.service.
Otherwise, you remount the remaining filesystems as read-only. After remounting read-only, the filesystem is clean. It is consistent on-disk; requires no repair operations; has no remaining writes cached or queued up in RAM.