The network would still create new blocks but wouldn't finalize them. Finalizing means they can't be undone without destroying a large percentage of the stake. Without finalization, you still reach a point where it's very unlikely that the block will be undone.

The non-responsive stakers would gradually lose their stake. The penalty for going offline is normally small, but if most validators go offline at once it's considerably larger. Their stake will shrink, until they don't hold most of the stake anymore and the network can start finalizing again.