Apple - OS X Security Update hangs during restart

Booting into Safe Boot and then installing the .dmg image of the update worked for me. If I tried to install it via the App Store my computer would get stuck even before displaying an estimated time remaining.

In the special case of Security Update 2019-002 for High Sierra and Sierra we might have to observe a special caveat:

Apple released an "incomplete update". What that means remains unknown in the details. But the end-result for this security update should be for Sierra, 16G1918; for High Sierra, 17G6030 in build numbers. Update failures may or may not be result of this "incompleteness".

In effect it seems advisable to not rely on the AppStore update process, but instead turn to the latest standalone installers available from Apple, for Sierra at https://support.apple.com/kb/DL1995

If installing from that DMG does fail as well, then the standard advice troubleshooting guides come into play:

Macworld: How To Fix A Mac Stuck Installing A macOS Update

1. Check Apple's servers
2. Switch to a wired connection
3. Cancel the download (to be able to restart it)
4. Download the software from Apple's support website (the DMG just advised)

After these are ensured:

1. Find out if your Mac has really frozen

2. Look at the Log to see if your Mac is still installing OS X

   Press Command + L. This brings up additional information and more details about the amount of time still remaining for the install. It may give you a better indication of what files are being installed and the amount of time left.

3. Wait (Macworld says "a few hours", I say after twenty minutes the Mac had a fighting chance I my time is limited

What to do if your Mac freezes during software installation If you're positive that the Mac isn't still working on updating your software then run through the following steps:

1. Shut down, wait a few seconds, then restart your Mac Press and hold the power button to shut down and start your Mac back up.
2. Go to the Mac App Store and open Updates If you were installing an app from the App Store, then open the App Store and click Updates. You should find that the update/installation process carries on from where it left off.
3. Check the Log screen to see if files are being installed When the progress bar appears, press Command + L again to check the Log screen and ensure files are being installed. If the Log screen shows that nothing is happening move on to the next step.
4. Try installing the Combo update As we mentioned earlier, the Mac App Store isn't the only place you can download Mac software from. Apple still hosts software on its website, so you can download it from there.

There's good reason to get your software from Apple's website if you're encountering problems: the version of the software available from the Mac App Store will only include the files necessary to update your Mac. If you go to Apple's support website you can find a Combo updater which includes all the files required to update the macOS. This version of the update will replace all the system files and thereby ensure the update is complete.

5. Install in Safe Mode Press the power button and hold down the Shift key to start the Mac up in Safe Mode. Open App Store and update your apps while in Safe mode. Reboot.
6. Make some room If the reason the update was failing was that there wasn't enough storage available to perform the installation then you might be able to delete some files in Safe Mode.
7. Reset the NVRAM If Safe Mode doesn't work, restart the Mac and hold down Command, Option, P and R. This will reset the NVRAM. Wait until the computer restarts and wait to see if it starts updating. For more information read How to reset the PRAM/NVRAM here.
8. Use Recovery Mode to reinstall macOS As a final option you could restart the Mac in Recovery Mode (hold down Command + R at startup). There are a number of options to choose from here - you could recover your Mac from your last Time Machine backup, or perform a disk repair - but we recommend choosing the 'Install new OS' option. We have a separate tutorial on how to reinstall MacOS using Recovery Mode.
   When it reinstalls macOS your Mac will replace all the Apple system files overwriting any problematic ones that may be contributing to this error - hopefully. This update won't include the latest version of the software so after performing the update, check Software Update and apply the latest macOS update.
9. Install the OS from an external drive If you're still having issues with the install you could try installing the OS from an external drive. Read this tutorial to find out how to install macOS on an external hard drive.
10. Run Disk Utility once you've updated When you finally get the software up and running we advise that you run Disk Utility to correct any issues that might have caused the problem in the first place.

SafeMode is really misplaced at only number 5. SafeMode runs an fsck on the root volume, clears out those ever self-corrupting caches and prevents unneeded-for-the-update-installation software like extensions etc from loading.

Summary

If an update fails

1. retry
2. retry with DMG updater
3. retry with DMG from SafeMode
4. retry after applying some voodoo from the Macworld list (NVRAM etc)
5. look for more desperate measures (restore from backup; re-install the system etc)