EIGRP includes a special type of hello packet, known as a "goodbye." Goodbyes are transmitted by an EIGRP router to its peer whenever a neighbor adjacency fails but the interface to reach that neighbor is still up. This could be the result of administrative reconfiguration, but sometimes the physical link between two EIGRP neighbors will fail without the routers realizing it (the interface status remains up/up).

In this case, the router will continue to transmit hellos (among other data) to the neighbor without receiving any hellos in return until the hold timer expires and the adjacency is torn down. When this happens, a router will transmit a goodbye message as an explicit notification that it is tearing down the adjacency.

%DUAL-5-NBRCHANGE: IP-EIGRP(0) 1: Neighbor 10.0.0.1 (FastEthernet0/0) is down:
Interface Goodbye received

You're likely to wonder what the point of this is if the link to the neighbor has failed. However, goodbyes provide an excellent troubleshooting tool when dealing with links that have only partially failed and have become unidirectional. This is a common scenario with fiber connections, and as I have come to find, with satellite links. Often one satellite station will be receiving from another, but for some reason (such as poor weather) will not be transmitting at a high enough power for its signal to be received by the distant station. When EIGRP is run across such a link, the distant station will tear down the adjacency and transmit a goodbye packet, giving the operator a clear indication of the direction in which the link is still functional.

The goodbye packet itself is actually a hello packet with all its K values set to 255. An example can be seen in packet #9 of this EIGRP traffic capture.