Is there a search engine where can the deleted historical information or pages there were removed from google search (or other search engines) can be found?
Google user can use caches link to see old/deleted webpages for any website. There is no any specific time duration for how much time, the cache files will be index on Google server, but if content is useful for user then Google might don't delete it for many years, otherwise they will delete it in few months.
If you own content then you can request cache to removal from Google search console, they just down it temporary for 90 days. so webmaster can use noindex, robots.txt and 410 http error together to remove it permanently. More information you can find out here.
But there are other cralwers as well, for example web archive machine, which crawl webpages and save it on their server, so any user can see how site was looking/have content in old days. To block such a cralwer find out their spider/bot/crawler name, and block it on your robots.txt
May be you mean internet archive