The supine position disgusted homeowners often find them in is a result of two domestic features: insecticides and flat floors.
Q. Why do I always find roaches dying belly up on my floor?
A. A roach that dies on its back may be the exception, rather than the rule, academic cockroach experts and exterminators agree. It depends on what kills it and on what kind of surface.
In the wild, roaches are more likely to die as the prey of birds or small animals, or possibly of old age, after an adult life span of 20 to 30 weeks for a female German cockroach .
If they are not eaten, they probably end up as random parts of the organic detritus on the forest floor.
In a domestic situation, a roach may find itself on a smooth floor of polished wood, tile or stone. With a relatively high center of gravity and a smooth, rounded back, a roach that gets turned over for any reason will find it very hard to right itself without twigs, leaves or other uneven features for its legs to push against.
And if the roach has been the target of an insecticide, certain kinds of poison, notably organophosphate nerve poisons, cause muscular spasms that can flip a cockroach onto its back. These nerve poisons can inhibit an enzyme called cholinesterase, which breaks down a neurotransmitter called acetylcholine. An excess of this chemical in the nervous system leads to the spasms and interferes with muscular coordination, leaving the insect trapped on its back as it dies. question@nytimes.com