Det finns inte mycket om vad som hände med drakar, men här är vad jag kunde hitta:
Dragons were created by Morgoth. Many of them died at the War of Wrath (at the end of the First Age. That is why there aren't a lot of dragons in the Thirds Age)
(J.R.R. Tolkien, Christopher Tolkien (red.), The Silmarillion):
During the War of Wrath, Morgoth unleashed a new terror upon Middle-earth -- the winged dragons. Chief among these was Ancalagon the Black. Eventually slain by Eärendil the Mariner, Ancalagon's fall crushed the towers of Thangorodrim. Many of the dragons were destroyed in the War of Wrath but some fled and survived into the later Ages.
Den största och mest fruktansvärda (nämnda) draken som bodde i tredje ålder var Smaug.
Gandalf sa till Frodo:
(J.R.Rol. Tolkien, Ringenes Herre, Ringets Sammanslutning, "Skuggan av Förflutet")
[...] there is not now any dragon left on earth in which the old fire is hot enough [to melt the Rings of Power]
indikerar närvaron av andra, mindre drakar.
(J.R.R. Tolkien; Humphrey Carpenter, Christopher Tolkien (eds.), Letters of J.R.R. Tolkien, Letter 144, (daterad 25 april 1954))
Vad vi vet från Ringen om Herren är att efter åldern började drakarna flytta norrut till Northern Waste .
It would appear that the dragons fled to the Northern Waste, far from the lands of Men and Elves. Over the centuries, the race of dragons continued to breed and repopulate, particularly in the Withered Heath, an area in between two spurs of the Grey Mountains.
(J.R.R. Tolkien, Ringenes Herre, Bilaga B, "Tredje Ålder", Bilaga A, "Durins Folk"):
In the late Third Age the dragons of the Withered Heath, stirred by the return of Evil, began to harass the Northmen and make war with the Dwarves around the year T.A. 2570 (Dáin I and Frór of Durin's folk were killed by a great cold-drake in 2589). It was perhaps in these wars that dragons swallowed four of the Seven Dwarf-rings.
Här är vad vi vet om Smaug (från Hobbit):
The most fearsome dragon of the Third Age was Smaug, who laid waste to the Dwarf-realm of Erebor and the nearby town of Dale. This devastated the area and sent Durin's folk into exile. Smaug remained in the abandoned halls of the Lonely Mountain for many years until the coming of Thorin and Company and their "burglar", the hobbit Bilbo Baggins. This began a chain of events that led to Smaug's death at the hands of Bard the Bowman.