Higher Learning: In the original timeline, the humanity has been wiped out and Shinji and Asuka has to raise a family on their own on a devastated world. The epilogue happens after Third Impact: the humanity has been wiped out during Instrumentality, but Shinji's choices allow people returning, and the world is slowly recovering.
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.
Scar Tissue: Most of Governments have been reinstated, and the half of world population has returned. However the major cities are in ruins, the roads are broken, the other half of people keeps missing and the returned ones are living on refugee camps as cities are being rebuilt, there is a lack of supply water, crops are damaged and there are riots due to the lack of food and water. In other words, the world has became ‘‘Kenshiro’’’s world.
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.
The Second Try: Chapters 2, 4, 6 and 8 are set here: Shinji and Asuka are the only humans left on the world and they must learn to survive and open up to each other.
Fallout: Equestria: This MLP fanfic - along with the countless Recursive Fanfics it has inspired - 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.