Suppose, not entirely hypothetically, that you use Apache and have an area of your website protected with Apache's HTTP Basic Authentication. A user comes to you with a problem report; while interacting with this area of the site, they unexpectedly got re-challenged for authentication. In fact, in your Apache logs you can see that they made an authenticated request that returned a HTTP redirect and literally moments later their browser's GET of the redirection target was met with a HTTP 401 response, indicating that Apache didn't think they were authenticated or maybe authorized. Unfortunately, our options for understanding exactly what happened are limited, because Apache doesn't really do logging about the Basic Authentication process.
There is one useful (or even critical) piece of information that Apache does log in the standard log format, and that is whether or not the HTTP 401 was because of a lack of authorization. Both normally get HTTP 401 responses (although you can change that with AuthzSendForbiddenOnFailure and perhaps should), but they appear differently in the normal access log. If there was a successful authentication but the user was not authorized, you will see their name in the log file:
If they are not authenticated (for whatever reason), then there will be no user name logged; the leading bit will just be '192.168.1.1 - -'.