security update

When you say it gets "stuck," for how long have you waited? This latest update on my older, slower laptop (late-2010 MacBook Air) took a very long time, more than 30 minutes, and the progress bars and "time remaining" indicators did not provide accurate information. Also, there appeared to be multiple restarts, and some very long "pauses" during the process. I am starting to believe that "a watched system update never completes," in other words, go away for a while, I would leave it for at least an hour. Similarly, on another laptop, a 2017 MacBook Pro, 10.14.6 (Mojave, not High Sierra), the latest security update required multiple restarts and took over 45 minutes. On the other hand, I have done some security updates in just a few minutes. So I would allow at least an hour before declaring that no observable progress is "failure" in an update.

In that case, I suggest you go back to BDAqua's suggestion and restart in Safe Mode. That eliminates most every possibility that some software or extension running on your Mac is preventing the computer from shutting down in the way it needs to in order to install the update.

If the Safe Mode approach (see BDAqua) does not work, then try resetting Parameter RAM.

If that doesn't help, I would recommend a hardware test, perhaps at an Apple Store, were they can see the behavior.

If that provides no answers, then I would suggest as a final resort something that I have actually done successfully, and that the Apple Store would probably recommend: namely, make two complete backups of your entire disk, one with Time Machine and one a bootable "clone," then boot into recovery mode and erase the disk and install a new operating system. On first boot, your computer will come up like a new computer and start the first run setup procedure, asking if you wish to migrate files from a backup. Migrate over just user accounts but no software. Start with just Apple-provided native software. Apply all software updates including this problematic one. I predict they will succeed. Then install other/commercial software from original disks or fresh install downloads. Only install what you really need. Check if you can that whatever you install is compatible with High Sierra. This last method takes ~ hours, but I have done it as a last resort with a stalled OS update and it did succeed. (MacBook Air late-2010)

Try installing it in Safe Mode...

Safe Boot from the HD, (holding Shift key down at startup), does the problem occur in Safe Mode?