My definition of a rare breed was any dog I hadn't actually met during the first 50 years of my life and after living in Wisconsin, Texas and California and traveling extensively.
Per this criteria, my family went to see a dog at a shelter 50 miles away that my wife had seen on a weekly spot on a local news program. She couldn't remember what breed she was but she thought "flat something." I thought maybe flat-coated retriever, which would be a rare enough find in a shelter.
What we found instead was a Plott hound. She jumped about five feet straight up when we approached her kennel and then dragged first me, then my son through the woods during a test drive. (I'm 6'2" and 220# and my son is bigger, younger and likely stronger than me.)
I was intrigued by her intensity, her strength and her bad attitude. I filled out some preliminary paperwork, which got me to the top of the list. But I had never heard of a Plott hound. I went home and read up and was both appalled and intrigued. Five days later she was mine.
It took six months before she decided she liked us well enough and several years before she became a dog normal people might invite to live in the house. Eventually, she became an intensely loyal and affectionate family dog.
Turns out Plotts are not particularly rare in Wisconsin because people in Wisconsin hunt bears. I can't imagine why. I never met one 'cause there aren't many used as house pets. You won't see one at doggy daycare or the dog park.
Here is an older, but still accurate, article about Plotts - right after they first appeared at Westminster. (Kind of like entering a Humvee in a Formula One auto race.)
The Plott hound, the ninja warrior of dogdom.
A somewhat uncommon breed that I admire greatly but will never own is the Rhodesian Ridgeback. Close as I'll ever get was Esther the Plott.