A passive shutdown system for a liquid metal cooled reactor may include a tube and a neutron absorber within the tube. The tube may be configured to extend through a core of the liquid metal cooled reactor. The tube has an upper end and a lower end. The tube defines a flow path for a liquid metal coolant. The neutron absorber is a mobile structure configured to partially obstruct a flow of the liquid metal coolant within the flow path. A method of operating a liquid metal cooled reactor may involve the use of the passive shutdown system.