Create page from plugin, but have it completely hidden

I need to have a plugin create a page that is publicly accessible, but does NOT show up in the admin section anywhere, and cannot be deleted or modified.

I thought maybe figuring out a way to have a publicly accessible page that doesn't really "exist" in the database might be the way to go, but I couldn't figure it out.

I just don't want any user to be able to delete or modify the page.