Is the congregational prayer valid if the imam's voice cut out during the first prostration in the last rak'ah, and those praying behind him in the back rows were unable to follow him, so they completed the prayer individually?

Your prayer is valid. As long as you caught one unit (rak'ah) of the Jum'ah prayer, you complete it as Jum'ah, meaning you complete the remaining two units, and do not complete it as four units of Dhuhr. Ibn 'Uthaymeen mentioned that if the Imam's voice cuts off and the congregant prays alone, his prayer is valid due to his excuse. If the sound cuts off during the Jum'ah prayer in the second unit, the congregant completes it as Jum'ah because he caught a complete unit. The congregant should not immediately intend to pray alone, but rather wait in case the sound can be restored.