The 'Establishment of persistence' stage of the cyber kill chain is where the attacker secures their foothold within the compromised system, often by creating backdoors or downloading additional malware. This establishes ongoing access, making it possible for attackers to avoid detection and continue their operations even if initial access vectors are closed. Other stages like Reconnaissance and Command and Control are either preliminary steps or control mechanisms but do not specifically focus on maintaining long-term access inside the threat environment.