I know many blogs that posted really good stuff a few years back but have become inactive now. I want to read the posts but it is very inconvenient to go to the blog’s website daily and read one post and remember which ones you have read. So, is there a service that can periodically deliver these old posts (say one per day or week) as an RSS feed/email?
RSS/ATOM feeds are generated by the website as @izzy mentioned up there. The related CMS allows you to select how many recent posts should be available in RSS feed link. If you select a big number, that'll generate a giant XML file which will make it tedious for the readers to access and browse the items, therefore the common thing with websites or blogs is that they choose to display a small number of the most recent items in the feed, e.g. 10, 20.
However there may be occasions where you might want all items in the feed URL. I was working on a podcast app that used the RSS link to parse and display the items, and I wanted it display all episodes of the podcast. What I did was to ask the blogger to change the number of items for the feed, save that XML file that contained all the items from the beginning up to now, and upload it on my own server. Writing a script, I could check the RSS link for the new items, and if any, have the script write it into the file on my server and keep it updated. Doing this, I'll have an XML/RSS link having all the upcoming items forever!
I know it's a bit complicated, but if you're planning to be able to read the current posts in the future, you can do something similar, but if you want the already-expired items in the RSS, then it'll be a bit difficult without getting in touch with the blog author.