Finding deleted blog posts/articles

I don't know if what I want to do is possible but I suspect if it is, someone here knows how.

I want to do some link building for a client. I have an article written for them and I want to find deleted articles on a similar topic that have backlinks.

Is there a way to search for pages that 404, based on what topic the page was originally about?

PS. as per a tag recommendations as I posted this, the expired article hunter software seems to be what I'm looking for. Is there a manual way to perform this by myself?

Have you tried web .archive.org yet? Sorry i can not add links!

There are chrome extensions that tell you which links are 404, so you can work the other way - search for articles on the topic, run the 404 checker, and then suggest to replace the 404 links with your article.

@CredibleZephyre It seems to me that what you want to do is what is known as 'broken link building'. There are many ways to do that, this is a good guide: https://ahrefs.com/blog/broken-link-building/