The goetia-shutdown service

goetia-shutdown is the service that starts system-shutdown-daemon. goetia-shutdown is down by default. Starting it initiates the shutdown procedure.

goetia-shutdown consists of three scripts:

run

stage3b tries to execute ./stage4, which is by default not executable. If it can not execute ./stage4, and only in this case, it continues with the following.
It makes ./stage4 executable.
It sends SIGCONT to all processes.
It sleeps for 1 second.
It writes a banner to its standard out.
It send SIGKILL to all processes.
This also stops the system-shutdown-daemon process. It is automatically restarted by the system supervision tree, but this time, both the files ./stage3b and ./stage4 are executable. Which leads to the execution of ./stage4.

stage4 reads the envdir at the shutdown-directive subdirectory of the system runtimedirectory using s6-envdir.
It reads the DIRECTIVE evironment variable, defaulting to -r, if DIRECTIVE is not specified.
It runs umount -A.
It remounts the root filesystem read-only.
It runs shutdown -o ${DIRECTIVE} now.

The entire shutdown procedure roughly works as follows:

This service, running system-shutdown-daemon gets the instructions from system-shutdown to shutdown.
system-shutdown-daemon does most of the shutdown procedure. Part of it is to make stage3b executable. In the end, system-shutdown-daemon sends SIGTERM to all processes but PID 1, including itself.
this service gets restarted automatically. system-shutdown-daemon now instantly executes into stage3b.
stage3b makes stage4 executable. Followed by sending SIGKILL to all processes but PID 1, including itself.
The final restart of this service causes system-shutdown-daemon to instantly execute into stage3b which instantly executes into stage4, which instructs the Kernel to do the actual halt, poweroff or reboot.