In that case the router will not show the neighbor in the routing table at all.Secondly,  In case a known neighbor goes down due to hello not  received from that neighbor  within dead interval; Even in that scenario the router will remove the neighbor from the neighbor table but will not show any DOWN state.So my query is that , in which kind of topology/scenario  we can see the DOWN state of ... (more)

If you dont have route in routing table, you can say when you interface is shutdown the neighbor will see down state.

If you dont have route in routing table, you can say when you interface is shutdown the neighbor will see down state.