"Postmortem fetal extrusion" is the formal medical term for the phenomenon known more colloquially as "coffin birth." Though it sounds a bit far-fetched, coffin birth is pretty much what it sounds like it is: a child is born to its mother after she has died, whether the woman is literally in a coffin or not.
When a woman is in labor, her body uses a series of contractions, often prolonged, to compel the baby to leave the womb and pass through the birth canal. This is the basic process of a live birth, and it is essentially the same process that happens during a coffin birth except for the contractions. In the case of a woman who has died and begun to decompose,
naturally occurring bacteria in the organs of the abdominal cavity (such as the stomach and intestines) generate gases as by-products of metabolism, ...[cause] the body to swell.
As the gases cause the woman's body to swell, pressure is placed on her womb and eventually the uterus is expelled from the body, including anything contained in it. At this point, of course, the odds of the child being born alive are virtually non-existent, so the term "birth" here does not necessarily imply life.
Before the late 1800s, incidents of coffin birth were much more likely to occur than they are today because that time marked the beginning of modern embalming procedures. Embalming fluids are used to flush out and replace the body's natural fluids, along with the bacteria which causes bodies to bloat during decomposition.
Before embalming became routine, incidents of coffin birth were recorded. In 1551, for example, a woman was hanged during the Spanish Inquisition and four hours later two dead children fell from her body as she was still hanging from the gallows. Other incidents of infant expulsion were recorded over the years, though again most of them happened before the woman's body was actually placed in a coffin and buried. Most occurred within the first day or two after her death and before she was buried. Finding an expelled fetus during an exhumation (a coffin removed from the ground for some valid reason such as a legal proceeding or a scientific investigation) has happened but is rare.
Nevertheless, some remarkable incidents have been recorded. A most astonishing incident of coffin birth happened in Toronto in 2009. A woman who was seven and a half months pregnant died from injuries she incurred in a car accident. Her body was kept in a morgue cooler for seventeen hours,
and covered with a simple burial shroud 20 hours after the accident.
Three hours later the cemetery workers were lowering her casket into the grave when they heard a baby's cry. The little girl had been expelled from her mother's womb and miraculously survived despite being deprived of any sustenance or oxygen from her mother. Though the baby was premature, dehydrated, and starving, she survived and is expected to live an entirely normal life (or at least as normal as possible, given her amazing experience).
While the term "coffin birth" is not particularly accurate for most cases, it does capture and explain the idea of this physical phenomenon.