Follow-the-leader (FTL) motion is essential for continuum robots operating in fragile and confined environments. It allows the robot to exert minimal force on its surroundings, reducing the risk of damage. This paper presents a novel design of a snake-like robot capable of achieving FTL motion by integrating fiber jamming modules (FJMs). The proposed robot can dynamically adjust its stiffness during propagation and interaction with the environment. An algorithm is developed to independently control the tendon and FJM insertion movements, allowing the robot to maintain its shape while minimizing the forces exerted on surrounding structures. To validate the proposed design, comparative tests were conducted between a traditional tendon-driven robot and the novel design under different configurations. The results demonstrate that our design relies significantly less on contact with the surroundings to maintain its shape. This highlights its potential for safer and more effective operations in delicate environments, such as minimally invasive surgery (MIS) or industrial in-situ inspection.