I tried to do this, at another user-database
*--------------
CREATE TABLE temp.user LIKE mysql.user
--------------

ERROR 1347 (HY000) at line 1: 'mysql.user' is not of type 'BASE TABLE'*

the idea was to duplicate the user table and backup the copy, but it did not work. Any idea?

you need to duplicate mysql.global_priv table, mysql.user is just a view over mysql.global_priv

THIS WORKS
mariadb-dump --no-create-info --skip-triggers --compact mysql global_priv > user.sql

but the question is if I execute the output

mariadb mysql < user.sql
will it work or not?
In general, how does anybody backup and restore the users for a mariadb system, so the company may quickly come back in case of a total catastrophe?

The backup and restore from table global_priv works, but I also need to backup all the Grants, otherwise I will have useless users. The grants for users are stored in what table?
The fact that I need to backup private tables is unusual. Mariuadb must have published and legal access to user data and grants.

if you execute

mariadb mysql < user.sql

it will work, in the sense, it'll restore the table as it was when you backed it up.

to backup and restore the users for a mariadb system you can either back up the system database,

mariadb-dump mysql

or

mariadb-dump --system=users

System tables are documented in the knowledge base.

The legal way to back up user accounts and grants without directly accessing system tables is

mariadb-dump --system=users