It only dies because without a mouth, it can't drink water. Cockroaches are supreme couch potatoes. They spend 75 percent of their time resting. Resting roaches point their antennae up and forward, and at about a 60 degree angle from one another. Cockroaches can crawl into some astonishingly small spaces.
Some female roaches incubate their egg cases in their bodies until they are ready to hatch.
These babies stay with their mothers a day or two after they are born. Picture a cockroach in a winter parka and mittens. Pest cockroaches can withstand freezing temperature of 32 degrees but will die if the temperature goes much below that.