Dwarves of the Blue Mountains
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After the War of Wrath, much of the Ered Luin fell into the sea, and stunted the mountains (such as the Dolmed, and Rerir. The Dwarf cities of Nogrod and Belegost, home to the Firebeards and Broadbeams were also ruined. Most of the two Houses left the Ered Luin for Khazad-dûm home of the Longbeards, bringing much lore and craft and swelling its numbers. Others stayed to build or rebuild their homes, and start over again.
For hundreds of years the remnants of the Firebeards and Broadbeams toiled in the Ered Luin. Possibly rebuilding Belegost at least somewhat, and maybe abandoned Nogrod. The remnants of the two Houses seemed to having largely moved to the Southern range by the mid-Third Age. They would have likely trafficked and traded with the Elves of Lindon (Second through Fourth Ages); The Men of Arnor (late Second Age through the Third Age); and of course with Durin's folk.
After (and probably before) the Balrog drove the Dwarves out of Khazad-dûm in 1981, the Firebeards and Broadbeams seemed to have went back to the Ered Luin and reinvigorated their old realms. Their may have also led to some tension with the Longbeards. However, the murder of their King Thrór of Durin's Folk changed this. The King's son Thráin sent messengers to all the Houses of the Dwarves requesting aid, and it can be assumed that both the western houses sent troops to fight in the War of the Dwarves and Orcs.
After the War, the remaining West Dwarves went back to their countries, and a year later King Thráin and his people established a new realm in the Northern Ered Luin; which may have possibly been given to them by their western kinsmen (It was part of their territory. His people prospered in a fashion, and were swelled in numbers by many of the wandering folk of Durin. They made things mostly of iron, trading with their neighboring kinsmen in the south, the Men of Eriador, and likely the Elves.
Years later after King Thorin Oakenshield went on the Quest of Erebor and was killed in the Battle of Five Armies, the Kingdom under the Mountain was re-established by the new king Dáin II Ironfoot. Many of the people of Durin's folk went to him and it became a great and prosperous kingdom once again. So a much smaller group of Durin's folk lived in the Ered Luin, if any. However the Firebeards and Broadbeams continued to live in their through the Fourth Age, and probably till the diminishing of the race of Dwarves (There were and always will be Dwarves on the eastern side of the Blue Mountains).