Quadrupedal robots have played a crucial role in various environments, from structured environments to complex harsh terrains, thanks to their agile locomotion ability. However, these robots can easily lose their locomotion functionality if damaged by external accidents or internal malfunctions. In this paper, we propose a novel deep reinforcement learning framework to enable a quadrupedal robot to walk with impaired joints. The proposed framework consists of three components: 1) a random joint masking strategy for simulating impaired joint scenarios, 2) a joint state estimator to predict an implicit status of current joint condition based on past observation history, and 3) progressive curriculum learning to allow a single network to conduct both normal gait and various joint-impaired gaits. We verify that our framework enables the Unitree's Go1 robot to walk under various impaired joint conditions in real-world indoor and outdoor environments.