You can NOT replace the slave_users and ask directly read the master_users because plenty of extension are directly calling the #__users.

The solution proposed by the Sharing of extension consists in creating a MySQL link between the slave_users and the master_users so that in fact the master_users is called each time you have a query in slave_users.

The result do exactly what you requested as the slave_users is simply a link and does not store anything.
This is the concept used in Jms Multisites and that is explained in the tutorial video 0.a
www.jms2win.com/tutorial#jms12x-0a

This is the concept of SHARING that we are using.
Store the information only once and share it.

You would have the MySQL Database tables sync then? Is there a sample code of how to do this?

There is no need to syncrhonize anything as MySQL create a link between the tables.
So there is no code sample.