Usually this question is asked by people running lists to which people are subscribed as a condition of their employment (corporate announcement lists, for instance). Sometimes it is asked by people who just don't want people to unsubscribe from their lists (typically spammers).

LISTSERV's design does not take this sort of thing into account, at least not by default. LISTSERV was designed as an "open" system (for lack of a better term) where subscribers had the ability to opt in and out of lists at their own discretion. So the answer is that there really is no simple way to stop people from signing off of lists, and the fact of the matter is that even if you did have such a feature available, if someone really didn't want to read your mail it would be simple enough for them to set up a filter rule in their mail client to automatically and silently dump the mail from your list into the trash.

Site admins who don't mind doing a little programming on their own can take advantage of LISTSERV's "list exit" extensibility to write an exit program to reject the SIGNOFF/UNSUB/LEAVE commands, but list owners who are not also site admins can't do this, since exit implementation is something that can only be done by a LISTSERV postmaster. (Note: List exits are only supported under LISTSERV Classic; they are disabled in LISTSERV Lite.)

However, the best way to handle this with LISTSERV is to create lists for mandatory mailings as Dynamic Query Lists (DQL) which can connect to databases or to your organization's directory server (e.g., OpenLDAP or Active Directory).  DQL lists do their recipient list pull "just in time" from your database/directory, based on a query you control.  Recipients can't unsubscribe from the list because the subscription list is not kept in LISTSERV.  DQL lists are ideal for things like campus security mailings, for instance.

(Note that creating a DQL list, or converting an existing list to DQL, will require your LISTSERV maintainer to set up and test the queries; this is not something list owners can do for themselves.)

LISTSERV sites integrated with LISTSERV Maestro can use a LISTSERV Maestro Hosted Recipient List set up so that only the admin can modify subscriptions.

The bottom line is that it is probably not worth the time and trouble to keep people from being able to sign off of any list, even if the list serves up highly-important data, given that it's always possible for an individual user to delete the mail unread either automatically or by simply dumping it in the trash after downloading it and reading the subject line.

It should also be noted that current law, for instance the CAN-SPAM act in the United States, and the more recent GDPR in the European Union, may require you to provide an unsubscription path for subscribers who wish to leave the list, particularly if subscription to the list is not required as a condition of employment/enrollment or similar, and/or if the list was not obtained through a double opt-in procedure.