chain.update(null);

        assertEquals(1, chain.updateCalls.size());
        assertNull(chain.updateCalls.get(0));
    }

    // Test update with multiple calls
    public void test_update_multipleCalls() {
        TestAuthenticationChain chain = new TestAuthenticationChain();
        User user1 = createTestUser("user1", "User One");
        User user2 = createTestUser("user2", "User Two");