Mac OS Sierra won't boot after installing an update. What to do?

Question

macOS

Yesterday I installed updates from the AppStore. Updates installed fine. Rebooted - everything worked. Then turned it off. Today I tried to turn it on, a screen for entering a login and password appears, I enter the password, the status bar reaches half and an error pops up - MacOS installation could not be completed, the last line in the log: auth failed to write file
What should I do in this case?

Answer 1

People are divided into two types: those who make backups and those who do not yet make them.
What type are you?)
Backup is the simplest.
If there are no backups, you can take another MacBook, connect yours to it, transfer data and reinstall the system. If there is no other MacBook at hand, for 1000 rubles everything will be thrown to you in any apple repair service.

Answer 2

Reinstalled the system via recovery mode (Command + R)
All data was saved, including programs. The only settings are off