The test jstests/replsets/auth_no_pri.js attempts to confirm that authentication is possible on connections to replica sets with no primary. It does so by creating a small replica set, adding a user and a data document, then taking down two of the three member nodes. The remaining node must eventually drop to secondary state, at which point the test attempts to authenticate and read the data document.

Unfortunately, the test does not express sufficient write concern when inserting the user and data documents, so it is possible for either of them to fail to propagate to the last node before the first two nodes are taken down.