The code to log off would be contained within the code on my Quit button. The
only times this could be bypassed is when a user closed Access using the
Close button in the Control Box (something a user will try only once!) or an
unexpected system shutdown or network interruption.

Since the only part that is running is the front end (obviously not a
client-server application), it seems to me that if a user lost his
connection, the next time the issue could be resolve is when he logs on
again. However, I cannot simply assume that a user's second logon is due to a
lost connection; otherwise, what is there to prevent many users using the
same ID? It seems like it would be best to just have a field in the users
table that can be reset by users having access to the form that contains the
field.

That's the administrative "unlock" field I was considering; a manual reset
of the LoggedOn field in the users table via a limited-access form.