The Pokemon story New World takes place some time after a yet to be specified event has wiped out human civilization. The main story takes place far enough after that that the main characters are not even aware that there ever was a previous civilization, and know nothing about the the end of it. A subplot about a girl who lived in that time period shows us more of what was happening back then.
A popular fan speculation takes the show's Schizo Tech and some apparently human-oriented objects (benches, tools, a train with a locomotive engine but is pulled by manual power) and draws the conclusion that Equestria is a distant post-apocalyptic Scavenger World built on the ruins of human civilization.
The Pony POV Series reveals Equestria's tribal history seen in "Hearth's Warming Eve" (and to an extent, the modern day as a recovered state), is this for the G2 world, whose late 20th century-level civilization collapsed when Discord's brother Destruction basically nuked the planet in order to prevent the creation of G3 and thus a Class X-4 Apocalypse. The "Gaiden: 7 Dreams/Nightmares" collection shows the immediate aftermath of this from the perspective of the main G2 ponies, and it definitely fits the qualifications of the trope.
Fallout: Equestria: This MLP fanfic takes place about 200 years after a magical-nuclear war between the zebras and ponies destroyed almost the entire world, and of what it takes to try and bring light back to the wasteland.
XoRax portrays Hyrule this way after a strange and unexplained plague called XoRax kills most of the population and mutates those who remain.
Harmony Theory: The Schism was an apocalyptic event which resulted in this.