How to stop a website from creating fictitious 404 pages

I got this email today

do you know how to stop a website from creating fictitious 404 pages that are building up in google webmaster tools and also appearing in awstats found in the cpanel.
these fictitious 404 pages are not real broken links found in my site ,, just something strange , mysterious in nature. please let me know if your exp. in this thank you.

I am answering this question in the video attached