If I understand correctly, in your scene light enters the room through the open door. If the door is closed, the room is dark, if open, is illuminated. In this case you cannot use GI cache. GI cache is used, if you have a static environment and static light. A cache is applied to dynamic objects that are moving in the scene. Try LPV - Light Propagation Volume. It is fully dynamic system of calculating the GI in real time.