Before revision:  This is achieved by introducing a quasi-Jacobian matrix which is asymptotically singular under higher-order local identification as well as weak /set identification; in these settings, standard asymptotics are not valid.
After revision:  This is achieved by introducing a quasi-Jacobian matrix which is asymptotically singular under weak or set identification, and when local identification fails. In these settings, standard asymptotics are not valid.