/usr/share/man/man8/systemd-shutdownd.socket.8.gz is in systemd 215-17+deb8u7.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/share/man/man8/systemd-shutdownd.service.8.gz
/usr/share/man/man8/systemd-shutdownd.service.8.gz