Context: Say Atropus (the World Born Dead) shows up in a campaign, very nearly causing a complete extinction of all life on your campaign world. Silver lining, the elder evil is repelled before the world dies completely, leaving small bastions of life scattered across the planet. The planet isn't incapable of hosting life, but it is quite hostile to it, what with all the undead roaming around. Vampires, Ghouls, and Illithids realize that without living mortals their kind dies out, so actively encourage mortals to slowly repopulate (you could say farming). Mortals survive but their place in the world is largely like that of larva in the outer planes.

So, what races would me most likely to survive such a catastrophic extinction level even and repopulate quickly enough to maintain a tenuous foothold.

I'm assuming the ever unkillable hosts of Goblins and Kobolds, perhaps humans through sheer grit and tenacity alone, but what other races do you think can reproduce quickly enough to teeter back from extinction?

Goblins, kobolds, hobgoblins, orcs, lizardfolk, bullywogs, and maybe humans (contrary to how they're commonly depicted in speculative fiction, humans actually reproduce fairly slowly).  Aarakocras have insanely short lifespans- they make goblins look long-lived, so odds are that they'd reproduce extremely fast as well.  And goliaths might also have fast reproduction rates given how they're typically depicted as a "live fast, die young" mentality.  Halflings are typically noted as having large families, IIRC.

Well ... there's no real answer. 

We have fluff telling us goblins and kobolds breed quickly, but that information isn't enough on it's own. If it's a race to breed the fastest, you need to do something akin to multiply the average litter size (basically 1 for humans) by the average number of litters born inside the fertile lifespan of a race, then divide by how many actually don't live to become fertile themselves. 

All of those are basically unknown. So any guess is good.

I'd like to point something else out: In any world where intelligent species (and some unintelligent) compete for a limited food supply, there will be war until things balance out. In other words, the undead will decline in number until they are few enough to sustain themselves on the living. Or, you know, alternatively they won't, all life dies, and the undead starve forever.

But ... goblins: Short lifespan, high infant mortality, they may not be the obvious choice they seem to be. I'd put my money on humans. Just to actually try to answer your question =)

Probably orcs - given that they overbreed already generating orc hordes on a regular basis, after them probably the goblinoids. They don’t generate hordes typically but there are always plenty of them. Humans would be next - between group think, long lives and a decent breeding rate they can probably rebuild population fast enough to match the orcs - but fertility rites would become a really big thing.

It is worth noting that birth rates are only part of the equation - adaptability and predator-prey dynamics will also play a part in survivability. Humans, for example, thrive in regular fantasy worlds not because they are the fastest breeders, but because they are the faster than dwarves and elves, while still maintaining physical and mental prowess over other faster-breeding or comparable races (ex. goblins breed faster, but tend to be self-destructive; halflings breed similarly, but their small stature puts them at a physical disadvantage).

Whichever race is excelling in your world would need to be something with the ingenuity to survive such a a harsh environment, preferably while not being a tasty morsel to the new undead predator class. Humans might be smart enough to survive in such a world - but they are also the most common snack to the undead.

Personally, I would probably choose at least two thriving races, who are thriving for different reasons.  Lizardfolk would be my choice for what you are going for - fast reproducing and able to quickly improvise tools and weapons, they canonically would be good at surviving an inhospitable environment.  Add to that the fact they are cold blooded and you have a good in-universe reason the vampires would not try to repress them and turn them into livestock. 

Other contenders - Locathah live underwater, and water is historically seen as a barrier against magical energy and creatures like undead. It is conceivable their society survived relatively unscathed, allowing them to fill the void left by other races.

I also would consider Sea Elves as a potential faction - though elves reproduce slowly, isolation on islands and protection of natural barriers could easily allow them to carve out bastions of their society which are divorced from the troubles of the rest of the world, giving you a very different take on success as a foil to fast-paced reproduction. Tritons could also fill the same role, though Elves are going to be a more recognisable culture to players. 

All life, yeah?  You're not asking about playable species, you're asking about mortal life, period.  You said "all life".

Generally speaking, any sufficiently small organism will have a very credible reproduction rate, so bacteria and various bugs should be fine.  In terms of the opposite, the world you're asking about probably no longer has whales and definitely no longer has trees.  The impact of that will ripple up the food chain, so apex predators, like most PC species, would have a big problem as their food sources dwindle.  Any obligate carnivores, like Tabaxi, are almost certainly going to just die of starvation.

I would say the most likely to adapt, overcome a hostile environment, and replenish their numbers, would be Humans. That's why they're the most wide-spread of the fantasy races, because their ability to do just that. Goblinoids might do ok for themselves, but they lack the organization (not to mention empathy necessary to care for other members of a civilization). While Lizardfolk are more adaptable, they tend to eschew larger civilizations in favor of their tribal structure, so following a calamity they're less likely to build back as quickly without that widespread cooperation. 

I would think Harengon reproduce pretty quick.  I'm assuming they breed like rabbits ;-)

Lycanthropes (if the curse is transferable by a bite in your world). Sent one to a normal village, and by the dawn you should have bunch of new ones. Due to their immunities, the normal village mob should be unable to deal with it.

Harengons, obviously.  They breed like rabbits...

Actually, it might be dwarves. they have a now higher reproductive rate, due to the thunderblessing, and they have the citadels to protect them.

Quote from quindraco >>

All life, yeah?  You're not asking about playable species, you're asking about mortal life, period.  You said "all life".

Generally speaking, any sufficiently small organism will have a very credible reproduction rate, so bacteria and various bugs should be fine.  In terms of the opposite, the world you're asking about probably no longer has whales and definitely no longer has trees.  The impact of that will ripple up the food chain, so apex predators, like most PC species, would have a big problem as their food sources dwindle.  Any obligate carnivores, like Tabaxi, are almost certainly going to just die of starvation.

 He said all races, not all life. And almost all races are playable now anyways.

Generally the longer lived a creature the slower they reproduce.

Generally the larger a creature is the less they reproduce.

The more advanced a civilization the less children they have because of their higher birth survival rate. Thus the modern western world. Third world nations still have as many children as they can give birth to just to replace losses before adulthood.

And remember that on a world that depleted of resources there will be a LOT of fighting between the different groups. Racism with be in everything. If your not from my village you will be suspect no matter what. You could be blamed for everything from the guards ingrown toenail to the sheep theft that happened a week ago. Trust will have to be earned and not given freely.

Cockroaches evolve quickly and become the dominant lifeform on the planet.

Ants make a better horror movie.

I'm amazed that no one has mentioned Thri-kreen and Plasmoids yet!

While I'm not aware of their reproductive habits, it wouldn't take much to imagine that they could be pretty prolific. Insects are notorious breeders, and plasmoids might be able to reproduce by mitosis.