In the UI, we have a feature called "Delete" which will remove Contacts from being visible. These Contacts are not fully deleted, just a soft delete. As such, they still exist and can be readded to the account. In the UI, this is all done automatically by advanced duplciate detection.
In the API, we expose all Contacts in the account so you can view and edit them. At this time we do not currently offer the same functionality in the UI to view soft-deleted Contacts.
Dave Berard Senior Product Manager, Constant Contact