In this letter, we propose an algorithm to check conditions of object caging when two fingers are grasping an object in a plane. Object caging is a method of geometrically constraining a movable range of an object by enclosing the object within end-effectors. Caging method has the advantage that an object can be trapped by only using its shape data, and accurate position control or force control is not required while the object is manipulated without losing. Therefore, a caging-based grasping can be achieved robustly even for objects in daily life environment without accurate models. In this letter, we study the properties of a cagable object while two fingers perform a non-surrounding caging on it. And, we propose a concept of Dual CC-Closure Region which can be applied on condition checking of object caging in reduced R² sub-space from SE(2) C-Space.