No really, there is no server. BerkeleyDB does not run in a separate process and there is nothing to start and stop. It accomplished all of these things without any server.
Ok, I bow to perrin's wisdom. It's not a server. It just stores and retrieves data and handles transactions and with an appropriate front-end (DBD::DBM on the low side and MySQL on the debatably high side) can be the backend of an RDBMS.