How to automatically install updates before shutdown?

Make sure you have the package unattended-upgrades installed, then configure the following options in /etc/apt/apt.conf.d/50unattended-upgrades:

// Automatically upgrade packages from these (origin:archive) pairs
Unattended-Upgrade::Allowed-Origins {
    "${distro_id}:${distro_codename}";
    "${distro_id}:${distro_codename}-security";
    "${distro_id}:${distro_codename}-updates";
    "${distro_id}:${distro_codename}-backports";
    "Canonical:${distro_codename}";
};

// This option allows you to control if on a unclean dpkg exit
// unattended-upgrades will automatically run 
//   dpkg --force-confold --configure -a
// The default is true, to ensure updates keep getting installed
Unattended-Upgrade::AutoFixInterruptedDpkg "true";

// Split the upgrade into the smallest possible chunks so that
// they can be interrupted with SIGUSR1. This makes the upgrade
// a bit slower but it has the benefit that shutdown while a upgrade
// is running is possible (with a small delay)
Unattended-Upgrade::MinimalSteps "true";

// Install all unattended-upgrades when the machine is shuting down
// instead of doing it in the background while the machine is running
// This will (obviously) make shutdown slower
Unattended-Upgrade::InstallOnShutdown "true";

// Do automatic removal of new unused dependencies after the upgrade
// (equivalent to apt-get autoremove)
Unattended-Upgrade::Remove-Unused-Dependencies "true";