Once the browser has it, they have it in their cache, and can regenerate it from the cache. It doesn't matter if it's still on the webserver or not.

As eibwen mentioned -- the file has to be available to the browser for it to be displayed. You have absolutely no control over what the browser can do with an image once they have it. (I've seen sites that use javascript so they can try to keep you from right clicking on an image, but that doesn't help someone linking directly to the image (not through the page you intended), or just turning off javascript.).