Autonomous navigation is a fundamental task for robot vacuum cleaners in indoor environments. Since their core function is to clean entire areas, robots inevitably encounter dead zones in cluttered and narrow scenarios. Existing planning methods often fail to escape due to complex environmental constraints, high-dimensional search spaces, and high difficulty maneuvers. To address these challenges, this paper proposes an embodied escaping model that leverages reinforcement learning-based policy with an efficient action mask for dead zone escaping. To alleviate the issue of the sparse reward in training, we introduce a hybrid training policy that improves learning efficiency. In handling redundant and ineffective action options, we design a novel action representation to reshape the discrete action space with a uniform turning radius. Furthermore, we develop an action mask strategy to select valid action quickly, balancing precision and efficiency. In real-world experiments, our robot is equipped with a Lidar, IMU, and two-wheel encoders. Extensive quantitative and qualitative experiments across varying difficulty levels demonstrate that our robot can consistently escape from challenging dead zones. Moreover, our approach significantly outperforms compared path planning and reinforcement learning methods in terms of success rate and collision avoidance.