Mystified by podcast behavior

For months now, when I've subscribed to a new podcast via iTunes, it ends up in a separate category from my older podcasts calls "not subscribed." I can access and play them, but I sometimes have to use the feed button to do so. In addition, I don't seem to be able to get rid of them once played, even by selecting "remove download." Maybe they're not actually taking up memory, but it does create clutter. Then the other day a podcast I'd been listening to for years suddenly shifted into "not subscribed," and to get the latest episodes I had to use the feed. What the heck is going on? Do I need to resubscribe to the "unsubscribed" podcasts? Will that lead to duplicates?