Imagine you were s two dimensional creature in a two dimensional plane. Width and length only, no concept of height. Let's say your world is like a piece of paper. Then, one day, a three dimensional create, 6 year old Thomas from Swindon, pushes s pencil through your piece of paper, your world. You have no concept of up or down. All you can discern is some disturbance in your field. Wouldn't that be spooky!
It's an interesting idea, but I had to look something up. Usually it's easy to distinguish whether to use the word plane or plain. This one was confusing. An abstract geometric would require plane, but this problem defines it as a real thing, which requires plain. So, I got stuck there.
It would be a source for curiosity wondering about where that bit of territory went. Because there is no up or down it wouldn't be a hole, just a circular piece of the plane I occupied would no longer be there. I suppose it would take on considerably more importance if that hole were punched where I happened to be. By the way, what have you been smoking?