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 enters their address in it, 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 interests, the lists they joined on that site, and can leave one list without leaving the rest. Manage lists in Email Campaigns, Lists.