When you archive a person from the Details tab on their profile page, a couple of new things happen.
Any future plan they are schedule to will be set as declined. In addition, the "Decline Reason" will show that it was declined because a specific person archived their profile on a specific date. (The "Replies To" person or team leaders will receive the decline email with the reason if they normally receive decline emails.)
Any plan that is in the past (archived) is not affected.
Any template they are scheduled to will be set as declined, and the decline reason will show in the Notes field.