Can a site get out of its place?

Question

HTML

Here usually serious things are asked, but a question has appeared in my head and does not come out. Forgive me for such a stupid question, but I dared to ask it here.
Can any content of the site / page crawl out of the window in the browser? Let's say something can be in the place of the bookmarks, or where the tabs are some kind of inscription. Or on the "Close" icon. In the most daring dreams and fantasies is this even a little bit possible?
Once again I apologize for such a question, but with shame I click "Publish".

Answer 1

Can any content of the site / page crawl out of the window in the browser?

Pop-up alerts. Used on many sites. See HTML5 Notification API.
Bookmarks can only contain bookmarks added by the user. The site cannot change the browser interface in any way. Is it just a little:
habrahabr.ru/post/245007
canonium.com/articles/html-meta-tags

Answer 2

The page title and favicon are displayed instead of tabs. Both of these elements can be controlled via js. You can change the favicon of the page to show the progress of the download or the number of notifications. Also the title.
But the element cannot "fly out" outside the visible area. For the browser renders content in a strictly designated area.
In mobile chrome, for example, there are special meta tags that repaint the browser window in the desired color.