Some extinct dog breeds are pretty wonky. The Turnspit dog was specifically bred to nicely fit into a kind of hamster cage, so that the dog would power a turning spit for roasting meats. Of course, the dog becoming obsolete led to its extinction.

https://en.wikipedia.org/wiki/Turnspit_dog

Having studied with a Coast Salish weaver, apparently there are some ongoing attempts to (re)create an analogous modern breed of dogs. Of course, the high accessibility and low cost of industrial wool yarn makes that the default for weavers carrying on this technique.

There's some really cool clothes and the like at https://slcc.ca/ - Squamish Lil'wat Cultural Centre - in Whistler BC.

> ...cozy sweaters made out of their beloved canine's shed hair.

https://www.thedodo.com/these-people-are-wearing-sweat-45331...

Indeed. But it's worth noting that these dogs were prevalent before sheep's wool was introduced to the Pacific Northwest. That's noted above the "extinction" section, but was a driving factor in the breed's decline as well. The industrial revolution aside, the need to preserve the breed's coat qualities for handweavers dropped off due to the introduction of other, superior fibers. Thus the cited cross-breeding with European dogs is very likely just a symptom of the other trends rather than a cause the breed was lost.