|Ictidosuchoides also survived the extinction|
How many there actually were rather depends on how big one has to be before being considered 'major'. Part of the reason that we can divide geologic history into so many periods and other subdivisions is that many of them ended with an extinction event of some sort, so that the creatures living afterwards looked different from those living beforehand. But that's not always the case, and, anyway, not all extinctions were equally large and dramatic - at least so far as we can tell from the fossils left behind.
At least five mass extinctions, however, fit into the most severe category, with particularly far-reaching impacts on world species diversity. The K-Pg event that wiped out the non-avian dinosaurs and ushered in the "Age of Mammals" is the most recent of these. Obviously, mammals survived that one, and did very well out of it, in the long term.
Going further back, the fourth mass extinction was the one that ended the Triassic period, and kicked off the Jurassic (there was a smaller event marking the end of the Jurassic, too). This would have been before the last common ancestor of all living mammals lived, but, taking a rather broader definition of the term "mammal", they first appeared during the Triassic, and, consequently, must have lived through that extinction, too. (In fact, the dinosaurs benefitted from it in much the same way that the mammals would the next one, becoming much more numerous once it was over).
The most severe mass extinction that we know of since the evolution of multi-cellular life was, however, the third of the "Big Five" - the End Permian extinction, 252 million years ago. This was undeniably before mammals, as we now understand them, existed. But the fact is that their ancestors had already diverged from the reptiles, so pre-mammalian not-actually-reptiles certainly did exist.
Back during the Permian, there had been a great many such animals, including some large and fearsome predators that may well have been more deadly than the dinosaur-ancestors they shared the world with. While some groups didn't even make it that far, almost all of those that did reach the End Permian event were wiped out by it.
Just three groups survived: the herbivorous dicynodonts, the carnivorous therocephalians, and the more varied cynodonts, which eventually gave rise to the true mammals. Why did they survive when, by some estimates, around two-thirds of all land-dwelling vertebrates didn't?
The answer to that will likely depend, at least in part, on what caused the extinction. Unfortunately, we don't really know the answer to that. Plausibly, Earth's ecosystems were already in a weakened state due to changes in world weather patterns when a couple of catastrophic events (major vulcanism, an asteroid impact, etc.) coincidentally hit in rapid succession. Or it could be something else; after such a long time, it's difficult to know.
One thing that we do know is that, after the extinction event, the world remained almost uninhabitably hot, dry, with unusually low levels of oxygen in the atmosphere. Clearly, this wasn't going to be much fun for anything, and it explains why it took such a long time for the world's ecosystems to recover. Whether or not these problems were part of the cause, or merely the result, of whatever happened (the former seems more likely to me, but who knows?) any animal surviving the extinction event itself then had to survive these unpleasant conditions if it was ever to leave descendants.
Presumably, different animals will have employed different tactics, depending on the exact conditions they found themselves in - the world is a big place, after all, and it can't have been the same everywhere. However, a new fossil may help to explain how at least one almost-mammal managed the feat.
The fossil in question belongs to an animal named Tetracynodon (literally "four dog teeth"), which has itself been known about since the 1940s. It's a therocephalian, a member of the group thought to be the closest relatives of the cynodonts, from which the true mammals are descended. During the Permian, some therocephalians reached relatively large sizes, and all seem to have been carnivorous.
Tetracynodon, however, one of just three therocephalian genera known to have survived through the End Permian Extinction, was quite a lot smaller, and it probably didn't eat anything much larger than insects. This alone may have helped it survive, requiring less food to sustain itself than its larger kin. How many later therocephalians may have been its direct descendants is unclear, but the group as a whole did survive for around another ten million years, diversifying to the point that some of them seem to have switched to herbivory.
Having said which, they had been extinct for millions of years by the time the first known dinosaurs evolved. That's how far we're talking in evolutionary history.
Many of the details of fossil mammals (or mammal-like creatures, in this case) are inferred from their skulls, and in particular their teeth. For example, a study of the nasal passages of the Late Permian therocephalian Glanosuchus suggest that it had the same baffles for retaining heat as true mammals - implying that it was warm-blooded. This, in turn, makes it more likely that the animals were hairy, rather than scaled or smooth-skinned, although that's something we're unlikely to ever know for certain.
In the case of this new fossil, however, what we have is a well-preserved front paw. So how does that give us a clue as to its survival strategy?
Well, the analysis of the bones, compared with those in the fore-paws of other therocephalians, and mammals in general, indicates that the metacarpals (the bones inside the palm) are unusually long. Then the first bones of the first two joints of the finger are short, while the bones in the fingertips are again, proportionately very long, with a good possibility that the animal had long and impressive claws in life.
Some of these features resemble those seen in living animals such as armadillos and sloths. What we know of the shape of the arms rules out a lifestyle at all like those of sloths, but armadillos might well be a better fit. The strong, sturdy shape of some of the bones also resembles that seen in potoroos, a kangaroo-like animal that is around the same size as Tetracynodon is thought to have been (around 40cm or 16 inches).
Both armadillos and potoroos use their forepaws for digging, and the suggestion is that Tetracynodon may have done the same. Certainly, it would not have been as efficient a digger as a mole, since the shape of the relevant muscle attachments is all wrong, but even an armadillo is still a pretty decent digging animal, scratching away at the dirt with its powerful claws.
The main reason that burrowing would be helpful to an animal trying to survive in the desolate conditions following the End Permian extinction is that it would allow it to shelter from the sometimes unbearable heat. In fact, a number of other animals from the same time show similar adaptations, and, in some cases, even clearer evidence of digging ability. Interestingly, many burrowing animals are also particularly resistant to low oxygen levels, which would also have helped.
Tetracynodon first appeared shortly before the End Permian extinction, so these aren't evolutionary responses to that terrible event. Rather, the suggestion is that it just so happened to have a lifestyle that spared it from the worst effects, huddling down in the soil away from the desolate hellscape above.
[Photo by "Rept01nx", from Wikimedia Commons.]