Can search engines add a link to a page that doesn't exist?

Question

Search Engine Optimization

Who knows, search engines can add a link to a non-existent page of the site in the search? At what for a long time any more does not exist.
Thank you!

Answer 1

Yes they can.
The page exists - it gets into the index of search engines.
After the page is deleted (returns 404, for example), then it is removed from the index after one or several updates of the PS,
but there is a nuance, if you somehow closed this page from indexing (robots.txt for example), then the PS will not be able to find out that the page has already been deleted and can continue to show it in the search.