Existence of Catholic Church without hierarchy

In case of a global catastrophe (nuclear war or something similar), a big majority of the global population would die, including pope, all bishops, all priests, all deacons. In all churches with apostolic succession (Catholic, Orthodox,...). However, there will be a small community of lay catholic people in one place. Let's say ten thousands, including theologically educated adults. What would be subsequent life of Catholic church? - Would catholic church exist? I am not asking on the sacramental life that would be most likely limited to baptism and matrimony only. I am asking whether we would speak about catholic church. Not just believers, but church itself. Are there any supportive or declining references in the official teaching of the church for "yes" or "no"?