Cloud applications expose - besides service endpoints - also potential or actual vulnerabilities. Therefore, cloud security engineering efforts focus on hardening the fortress walls but seldom assume that attacks may be successful. At least against zero-day exploits, this approach is often toothless. Other than most security approaches and comparable to biological systems we accept that defensive "walls" can be breached at several layers. Instead of hardening the "fortress" walls we propose to make use of an (additional) active and adaptive defense system to attack potential intruders - an immune system that is inspired by the concept of a moving target defense. This "immune system" works on two layers. On the infrastructure layer, virtual machines are continuously regenerated (cell regeneration) to wipe out even undetected intruders. On the application level, the vertical and horizontal attack surface is continuously modified to circumvent successful replays of formerly scripted attacks. Our evaluations with two common cloud-native reference applications in popular cloud service infrastructures (Amazon Web Services, Google Compute Engine, Azure and OpenStack) show that it is technically possible to limit the time of attackers acting undetected down to minutes. Further, more than 98% of an attack surface can be changed automatically and minimized which makes it hard for intruders to replay formerly successful scripted attacks. So, even if intruders get a foothold in the system, it is hard for them to maintain it.