I've seen these kind of characters before, especially the ones who say they are the "last one" of their family/pack/pride. I've seen a few say that they were "the last" of their species, but it's rare. Even I have had a few of my characters believe they were the last of their kind.
A long time ago, I once had a thylacine character who thought she might be the last of her kind. Whenever others would ask if their were any other thylacines like herself, she would reply, "I haven't seen any. I might be the last of my kind for all I know." But she was still hopefull that she would one day encounter other thylacines like herself out in the world. She never declared that she was the last thylacine, because she didn't know if she really was or not.
My unicorn fox character Amalthea... even though she is based on "The Last Unicorn" she isn't the last of her kind. People would ask, "are you the only unicorn fox left in the world?" she would respond in her Frenchy voice, "Of course not. I couldn't be zhe last of my kind. Zhere are ozhers like myself out zhere; you just need to know where to find zhem." She really isn't the last of her kind like in the book/movie. Her kind is somewhat rare and secretive.
I don't have any characters that claim to be the last of their family/pack/pride/clan. But I've seen many characters that claim that their entire family/pack/pride was killed in some kind of disaster, slaughter, war, or a plague of illness, etc, and how they were the only ones to survive. To me that seems pretty common and somewhat cliche. But the only thing that really irks me is when a character constantly sobs about being "the last of my family" to others repeatedly. And when people don't say the lines of, "I'm so sorry for your loss" they throw a big fit over it. "OH YOU'LL NEVER UNDERSTAND MY PAIN!" kind of rage. Get a grip, will ya?
So yeah...