No, it is not true that one cockroach can kill all remaining cockroaches. Cockroaches are known for their resilience and ability to adapt to various environments, making them difficult to eradicate completely. While some species of cockroaches can exhibit cannibalistic behavior, it is not an effective method for eliminating an entire population.
Cockroaches reproduce quickly and tend to live in large groups or colonies. If you have an infestation, it is unlikely that a single cockroach would be capable of killing all the others. Effective pest control typically involves a combination of strategies such as proper sanitation, sealing entry points, eliminating food and water sources, and using targeted insecticides or traps specifically designed for cockroach control.
It's important to note that addressing a cockroach infestation may require professional pest control services, as they have the expertise and resources to handle such situations effectively.