EIGRP is a distance vector routing protocol that is characterized by the fact that it sends incremental updates, and only when an actual change in the network has occurred.
My statement was written in order to emphasize the fact that EIGRP will send an update only when there is a change in the network (and not periodically like RIP does for example). Now the question that was asked was about a specific topology and about a very specific failure. That’s why I used the example of the loopback failing.
To clarify, yes it is true that EIGRP routers will send updates about any changes that occur in the network, whether directly connected, or learned via EIGRP updates from other routers.
The very first update will be sent by the router which is directly connected to the failed link, but that change will propagate from router to router until the whole network is informed, and alternative routes to destinations are calculated.
Thanks for mentioning it, and I hope this has clarified my statement.