A recent innovation in Japan is a battery-powered system (since 2016, click picture for details).

A new Suspension Monorail - even with battery backup of a mains-powered system - is unlikely to have a significant problem. The carriage would simply go to the next station to let passengers alight normally. Wellingtonians are familiar with such a system, if they had travelled on its (now decommissioned) trolleybuses in recent years. The buses would occasionally have to negotiate a length of overhead wire that had lost its power, and the bus would change over to battery power for a relatively short distance, then resume under mains power.