It is common for a listserv to file a copy of all the messages from the past month into one file. This allows new subscribers to request a file and read past discussions. It also means that you don't have to archive your own messages. You can read and delete them. Then, if you find a need to go back and find a message, you can request the stored file and find what you are looking for.
Archives are available for many discussions.
Usually, when you subscribe to a listserv, you will receive an introduction to the listserv message which will give you more details on accessing the archives. Currently, we have around 1000 newsgroups. The messages could add up to dozens per day, could clog up your mail folder or at least snow you under. You don't have to read every message, just select the ones whose subjects interest you. If there is more than one person on campus who would like to read the messages, each message is received by the College only once and everyone on campus can read it.