Is it true that if you stand on a cockroach it lays its eggs?

Cockroaches (or shouldn't that be "henroaches"?) do not lay individual eggs. About 20 eggs are massed together in an egg case called an ootheka. If you crush the roach, the egg case may survive because the roach carries it around for a time as it hardens. If you don't crush the ootheka, it may eventually hatch. If the eggs are still inside the roach, they stand little chance of survival because they will rapidly dry out without the protection of the ootheka.