This paper presents the architecture for a selfstabilizing hypervisor able to recover itself in the presence of Byzantine faults regardless of the state it is currently in. Our architecture is applicable to wide variety of underlying hardware and software and does not require augmenting computers with special hardware. The actions representing defense and recovery strategies can be specified by a user. We describe our architecture in OS-independent terms, thus making it applicable to various virtualization infrastructures. We also provide a prototype extending the Linux-based hypervisor KVM with the self-stabilizing functionality. These features allow augmenting KVM with robustness functionality in the coming stages and moving to cloud management system architectures such as OpenStack to support more industrial scenarios.