It's called a population bottleneck, where a near extinction event forces almost all individuals to share a large proportion of their genetic material, and the most recognizable example is in cheetahs.
It only applies to mitochondria, not the genes in the nucleus or anything constructed from those genes.
It's only unique because the "MR" in MRCA stands for "most recent".
You could have a species that's a million years old with an MRCA that's only 500 years old. You could also have a species with no MRCA. (As in, the only way to find an MRCA is to trace back into ancestor species.) Picture two islands where only males travel between them.
Consider the hypothetical population consisting of two people, whose fathers were both first cousins and whose mothers are second cousins, on their mother's... side.
Their mitochondrial MRCA is their great-great-grandmother on their mother's side, but their MRCA's are their great-grandmother (and great-grandfather) on their father's side.
The entire human family tree is like that, but way, way more complicated.
Speciation events tend to look more like, imagine you take a town of two thousand people and send half of them to the moon for a million years. The moon men and the earth men would evolve into two different species; if you looked really hard, you could find a single common ancestor from whom everyone in that town descended, but it's not like one of his children went to the moon and one stayed on earth; some of his great-great-*-grandchildren went to the moon and some stayed on earth. The common ancestor was hundreds or thousands of years before the population split in two.
Moreover, breaks don't always happen cleanly. Imagine for the first ten or hundred thousand years someone from earth would occasionally migrate to the moon or a moon man would return to earth. The same thing would have happened with proto-humans and proto-chimpanzees: long after the two species had begun to diverge they would still be interfertile, and some mating (or "gene transfer", if you prefer) would still happen long past the point you'd begin calling them two different species. Eventually the two species would stop being mutually fertile or even attractive and the rift would be complete, but look at how many big cat and horse-like species can still occasionally pull it off.
Evolution is messy, and the bush of life is complicated.