Well... probably most of the customers have been rebooked with another airline on the same date of departure, maintly partners like Alitalia, Air France and KLM via any other airports. If they have had the possibility of sending them, I believe thay will have done it.
when a passenger is transfered to other flight, the inventory should have been updated automatically as the reservations are being changed.

I am absolutely sure that Delta has a great over the counter team that resolves this kind of interruptions of the service, and at the time that the plane didnt take off bound to Rome, all the process began even without the knowledge of the customers. And this is a real dissaster when you are standing by on a flight that looked good, and other airline send their customers to your flight because of a cancelation, and the fill everyseat with interrupted passengers, so you are not accepted.

And that is done every single day, at every departure, with every connecting passenger, so no fear for tomorrow. In Iberia we call it the Recovery Service in the Hub Control department of Operations Control.

Hope this helps.