How will cockroaches be alive when human beings die?

Cockroaches are highly resilient creatures that can survive in extreme conditions, including radiation and scarcity of food and water. Their ability to adapt to various environments and their simple biological structure allow them to endure situations that would be fatal to many other species, including humans. Additionally, cockroaches have been around for millions of years and have survived several mass extinction events, making them well-equipped to survive in a post-human world.