Collapsing terrains, often present in search and rescue missions or planetary exploration, pose significant challenges for quadruped robots. This paper introduces a robust locomotion framework for safe navigation over unstable surfaces by integrating terrain probing, load-bearing analysis, motion planning, and control strategies. Unlike traditional methods that rely on specialized sensors or external terrain mapping alone, our approach leverages joint measurements to assess terrain stability without hardware modifications. A Model Predictive Control (MPC) system optimizes robot motion, balancing stability and probing constraints, while a state machine coordinates terrain probing actions, enabling the robot to detect collapsible regions and dynamically adjust its footholds. Experimental results on custom-made collapsing platforms and rocky terrains demonstrate the framework's ability to traverse collapsing terrain while maintaining stability and prioritizing safety.