Yes, we need to keep their existence and data for IT historical purposes, but when a faculty member leaves employment, we really need to just disable their login.
So I need a programmatical way to do that through the API.
While everything said above does provide you the information you need to modify a users account upon them being terminated or just need disabled. I must ask if your school is using an authentication method other than Canvas (LDAP, SAML, etc.)?
If you are using one of those methods then you would not need to modify anything within Canvas upon them leaving your school as once they have been disabled in those systems they would no longer be able to access Canvas either.
One thing you might want to do that I have done for my school is remove the forgot password option from the Canvas login page. I did this because this removes the users ability to reset their password and use Canvas authentication all together.