It's different for different podcasts.
Some podcasts only keep a few episodes in their feed - I think This American Life does this. If you want to listen to older episodes of This American Life you need to go to their website, where, if I recall correctly, you can stream anything but can't download (or maybe you can pay to download?) older episodes. Or you can download their app and stream through that.
Other podcasts keep all of their episodes in their feed, and for those podcasts you can probably use iTunes to get anything they've ever recorded.
Other podcasts also keep all of their episodes, but over the years they've accumulated so many episodes that iTunes won't have them all (maybe the maximum is 500?). For those podcasts, such as Stuff You Should Know, you can go to their website and download older episodes.
General note on podcasts: I've found iTunes and iOS very unreliable about keeping podcasts, no matter what your settings are. There have been a bunch of posts over the years here about people suddenly losing hundreds of hours of podcasts that were supposed to be kept. If I want to keep a podcast episode, I change the Media Kind to Audiobooks (using iTunes on my computer), and organize them that way.
