What happens when a subscriber signs up for a second list?

A signup block can point at a specific list (a drop alert, an event list). When someone who is already subscribed joins from its button, they are added to that list and stay on every list they were already on. The request is recorded on their contact, and nothing is sent twice.

An address that has unsubscribed is never re-added by a form. The form tells them so and points them to the link in any past email, where re-subscribing is their own explicit choice. On the site's member page, a signed-in member sees Your emails, one checkbox for each Email Topic the website offers, and can turn one off without leaving the rest; any other list they joined shows below with Leave. Manage lists in Email Campaigns, Lists.