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.”
Invoked: Evil Emperor Evulz massacres Gy’nary’s entire race in an effort to recruit him as his Dragon; Gy’nary is either unaware of that plot, or has no choice but to accept.
Exploited: Gy'nary uses his last of kind status as a Tear Jerker exploit to make people pity him.
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.
Bar Patron: That man over there is the last of his kind, dude. He’s shut himself off and rather’d die alone.