Cover it Up/ Remove : Main Subject

So much of photo is about remembering something forever and capturing the moment. 

What happens when you don't want that? What happens when you intentionally remove, or cover up the main subject. is it still recognizable? Does the image still have power/impact? Does it still say the same thing? Does it still say what you want it to say?

Does it defeat the purpose of photography? What is the point of an image if it doesn't reveal or remember something? 

Explain.