“Asshur (Assyria) is there and all her company, his graves are round about him. All of them slain, fallen by the sword. Whose graves are set in the uttermost parts of the pit. And her company is round about her grave, all of them slain, fallen by the sword, which caused terror in the land of the living.”
Assyria had caused terror in the land of the living, but now she is silent in the grave. It is twice stressed that she and her people are gathered there, slain by the sword. Israel had good cause to be pleased about that. Assyria had been a bitter enemy and a cruel overlord. They were the mighty empire destroyed and taken over by Babylon.
Of course Assyria still flourished above ground, although subject to Babylon. The idea would seem to be that the Assyria of the past, the powerful overlord, had died, along with those slain by Babylon, those who had once distressed Israel.