What is the historic reason behind this?
Of course it didn't start out as a border with Nunavut, but instead a murky border with Rupert's Land, which "belonged" to the Hudson's Bay Company. Much later, a more precise border between Canada and Newfoundland was made.
(I used to do this as a kid: Make up fantasy maps at a small scale in pencil, then enlarge them with a photocopier and trace over the fat lines with a narrower pencil, fabricating new "precision". It was great fun.)
It goes all the way back to 1763, at the end of the French and Indian War, when France ceded most of its possessions in Canada to the British.
This included the Labrador coast, whose principal economic asset (to the British) was a fishery. The British wanted to make sure that the French didn't steal their fish. Some things never change.
So in the Proclamation of 1763 (the one that started all the trouble down south), George III put the fishery (and some religious settlements on the coast) under the control of the closest colony, Newfoundland:
And to the end that the open and free fishery of our subjects may be extended to and carried on upon the coast of Labrador and the adjacent islands, we have thought fit, with the advice of our said Privy Council, to put all that coast, from the river St. John's to Hudson's Straights, together with the islands of Anticosti and the Madelaine and all other smaller islands lying upon the said coast, under the care and inspection of our Governor of Newfoundland.
The northern tip of the "Labrador Coast was defined as the entrance to "Hudson's Straights", which was determined to be the easternmost extent of the Hudson's Bay Company's control.
All the land given to Newfoundland was transferred to Quebec in 1774 but the Labrador Coast was returned in 1809.
In the meantime, the Dominion of Canada was created, but it didn't include Newfoundland, which remained a separate British colony. The Hudson's Bay company ceded Rupert's Land to Canada. Quebec was split off from Lower Canada and bits of Rupert's Land were successively given to Quebec (and Ontario, Manitoba, Saskatchewan, and Alberta, but that's not relevant to thus story).
The remainder became the Northwest Territories.
But the border with Newfoundland was still murky.
Just like all such borders created at this time, these borders were ill-defined and open to interpretation, and of course unsurveyed.
It was unclear how far in from the "coast" Newfoundland's control extended, and the precise location of the "Entrance to Hudson's Straits" was anybody's guess.
So several border disputes with Quebec later, Canada and Newfoundland decided to get the British Privy Council involved in resolving the dispute.
(I'm not sure what they were thinking. The British had just been the broker in a border dispute between the United States and Canada over a similar "coastal" definition, the result of which was handing the Alaska Panhandle over to the United States.)
The Privy Council looked over the documents and in 1927 handed a large swath of the Labrador interior over to Newfoundland. At the northern tip, the "Entrance to Hudson's Straits" was precised as Cape Chidley on Killinq Island. Since the Northwest Territories and not Quebec controlled Killinq Island, this meant a short land border between NWT and Newfoundland.
Newfoundland was finally admitted to Canada in 1949. The borders decided in 1927 were used, and Quebec wasn't happy, but of course they wouldn't be.
When Nunavut was created in 1999, it inherited most of Killinq Island from NWT and the small land border with Newfoundland and Labrador.
The Labrador Boundary: https://www.heritage.nf.ca/articles/politics/labrador-boundary.php
The Labrador Boundary 1927, Canadian Bar Review 335, sourced at https://www.canlii.org/en/commentary/doc/1927CanLIIDocs81