In Jain cosmology, time is cyclical, not linear. The universe goes through repeating half-cycles. Each half-cycle ends in a pralaya (dissolution) of the world, after which a new cycle begins afresh. So, yes—the current cosmic age runs through a succession of eras, and at the end of a half-cycle the world is destroyed and then re-emerges in a new beginning. The beings at that moment are not living through memories of previous eras in the way we think of human history today; the pralaya marks a complete dissolution, and the next cycle starts anew with a purer state before beings again populate the world.

If you’d like, I can explain the specific terms for the two half-cycles (utsarpiṇī and avasarpiṇī) and how Jain scriptures describe what happens at the end of each.