Dwarves of the Blue Mountains
After the War of Wrath, much of the Ered Luin fell into the sea, taking the Dwarf cities of Nogrod and Belegost homes to the Firebeards and Broadbeams with it (it then became the Gulf of Lune). Most of these two Houses left the Ered Luin for Khazad-dûm home of the Longbeards, bringing much lore and craft and swelling its numbers. While some stayed to build or rebuild their countries, and start over again. For hundreds of years the remnants of the Firebeards and Broadbeams toiled in the Blue Mountains. Working the mines and building new halls and mansions. The two Houses lived mainly in the Southern range after the Elder Days.
They most likely trafficked and traded with Elves of Mithlond during the Second through Fourth Ages, with the Men of Arnor in the late Second Age through the Third Age, and with Durin's folk throughout the their histories.
After (and possibly before) the Balrog drove the Dwarves out of Khazad-dûm in 1981, it is likely that the Firebeards and Broadbeams went back to the Ered Luin and reestablished their kingdoms. And had a lesser amount to do with the Longbeards except through trade. Until the murder of their King Thrór. Who was killed by Azog the Chieftain of the Orcs of the Misty Mountains. The King's son Thráin sent messengers to all the Houses of the Dwarves requesting aid. All the Houses sent troops and helped fight in the War of the Dwarves and Orcs. After the War the remaining two Hosts of the West went back to their countries, and a year later King Thráin and his group of Durin's folk established a new realm in the Northern Ered Luin, possibly being told of those lands by the Firebeards or Broadbeams. 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 neighbors to the South and to Durin's folk and other peoples elsewhere.
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 reestablished 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, but the Firebeards and Broadbeams continued to live in the Ered Luin through the Fourth Age, and Probably till the diminishing of the race of Dwarves.