Cockroaches do not lay eggs after they have been squashed or killed with pesticides as the egg sack inside of them will have been squashed as well. However, squashing a cockroach to death is not as easy as it may seem. Cockroaches are capable of flattening themselves out to hide under rugs and other items without attracting attention. They can also do this under a shoe or boot. This means that you can try stomping on them but that may not kill them. If you want to deal with a cockroach infestation trying to stomp them to death is the least effective way of doing it.
Cockroach dangers
Cockroaches are a dangerous and serious infestation. It is not a joke and is not something you can ignore because you do not see many of them. Cockroaches live in sewers and are coated in dangerous bacteria and viruses including Staphylococcus or staph infections which are severely dangerous and can also cause respiratory illnesses through the shedding of their carapace or moulting as they grow in size from birth to adulthood. This is very serious and can kill someone with a preexisting respiratory illness like asthma. Ignoring an infestation because it looks small will have long-term destructive effects on your health that will shorten your life.
Cockroach treatments
Treating a cockroach infestation that has been around for a long period can take a. Lot of work. Trying to do it domestically, and by that, I do not mean stomping on them but treating them with domestic chemicals may not be as effective as calling a licensed exterminator to do a commercial treatment. The general rule is if you are trying to treat it as an infestation domestically and have not resolved it within one month then you need to call a professional. Especially with cockroaches the health dangers are too severe to risk having the infestation continue.
Domestic Treatment
A domestic treatment usually contains three methods used in unison. Insecticide dust which is silicone dioxide and can be found both in synthetic and natural states can be used to kill cockroaches through physical contact. The dust, while safe for humans and animals, is dangerous to insects as it can catch in the limbs and scratch the waxy layer of the carapace and cause the insect to dehydrate and desiccate. This is a powerful chemical and highly effective in dealing with infestations but is not enough on its own. A spray pesticide added to the treatment will affect other cockroaches like babies who may not get harmed by the dust as they tend not to travel around like adults.
Commercial treatment
You can spray chemicals like permethrin sprayed around baseboards and around the counters in the kitchen and bathroom as well as inside of the motors of the large appliances and in the vent of the microwave you will hit another group of cockroaches, the babies that are often not affected by dust. Adding to that a treatment using bait can complete the process and get rid of a moderate to light cockroach infestation.