What should the worshippers do if the Imam loses consciousness during prayer and does not appoint anyone to succeed him?

If something happens to the Imam that prevents him from completing the prayer, the congregants have the choice between appointing one of them to complete the prayer with them, or praying individually, or some of them praying in congregation and others individually. All of that is permissible. Some scholars, such as the Malikis, have made it obligatory to appoint a successor in the Friday prayer.