Zig-zagged: Gy’nary is constantly cloned, and his clone is repeatedly killed off.
Averted: Either others of Gy’nary’s species are seen, or it is mentioned that there are others early on.
This trope can be a viable method of generating sympathy for a character…
…or, on the villainous side, an excuse for his evil deeds.
Lampshaded: “Don’t you dare feel sorry for me just because I’m the last of my kind.”
Evil Emperor Evulz massacres Gy’nary’s entire race in an effort to recruit him as The Dragon; Gy’nary is either unaware of that plot, or has no choice but to accept.
Evulz drips trillions of trillions of nukes on Gy'nary's home planet of Gy'nish to make sure his species is annihilated.
"Alright folks, the Gy'nishian Hunt officially starts now. Remember, every severed head you bring in will be reimbursed for two hundred dollars as well as a raffle ticket for a chance to win the new car."
Gy'nary uses his last of kind status as a Tear Jerker exploit to make people pity him.
Gy'nary is worth millions of dollars, and is eventually sold as a pet to some trillionare.
"Step right up, step right up! Welcome to P. T. Barnum's museum of curiosities. Now I will show you our star exhibit; Gy'nary, the last of his kind!"
During his escape from the Earth-Shattering Kaboom, Gy’nary put his sister (or another fertile female of his race that he knew) in suspended animation so that there will be a chance of his race repopulating elsewhere.
Emperor Evulz makes sure there are no survivors when he exterminates Gy'nary's race.
Scientists clone Gy'nary multiple times to bring his species back from the brink.
Bar Patron: That man over there is the last of his kind, dude. He’s shut himself off and rather’d die alone.