This study develops a mathematical framework to evaluate whether a rigid flat-foldable origami structure will unravel completely, partially, or not at all when pulled from two points. Starting with single-vertex designs, the study introduces geometric theorems based on crease intersection and torque from the line of tension. These are extended to multi-vertex structures by incorporating stacking constraints, angular rotation, and degrees of freedom. The result is a deterministic algorithm that predicts unraveling behavior from crease patterns alone, offering practical applications in deployable systems, robotics, and material science.