BSP trees and objection collision

Hello,

I have a question about the BSP tree algorithm. Lets say I have an environment and there is a room. Now I am partitioning that room with a hyperplane. That hyperplane is infinite. And that’s where I have understanding problems. Lets say there is an object outside of that room it could still intersect with that hyperplane that is partitioning that room because it is infinite. Like I have drawn in the picture below. So wouldn’t give that a wrong object collision?