I had this issue (iMac 21.5 inch, Late 2013 model) in mid-December and tried the 10.13.2 update again just now (December 30, 2107), and it failed both times in a similar fashion: Progress bar just halts 80 percent of the way through the update and it stays that way. Last time, I was able to "restore from Time Machine back-up" (external drive) by using Recovery mode. That is a 3.5 hour process, in my case.
However, I just discovered (in another thread) a way to avoid the 3.5 hour restore. This may not work for everybody, but it is worth noting:
Restart system in Safe mode (holding Shift as you restart). That allowed me to boot up. Then click Restart again. That gave me a restart that failed, with the screen message saying: "macOS could not be installed on your computer. The path /System/Installation/OSinstall.mpkg appears to be missing or damaged."
With that warning still active, I am able to select Apple Logo at top left and click the option to select "Startup disk..." Select old OS (10.13) and click "Restart." This gave me back my system before I attempted the update. I didn't know this existed, but it's very helpful.
I will NOT try this 10.13.2 update again. I will wait for the next update and hope it doesn't freeze my system while installing, something that has never happened to me in many years of updates.