Assuming there are open connections through an active system's virtual servers and a fail over occurs, by default, what happens to the connections.

By default, without connection mirroring enabled on virtual servers, the standby system does not have the state information for existing connections. Therefore, when a failover happens, all active connections through the virtual servers are terminated as the new active device cannot resume them.

Maintaining all open connections is not the default behavior; it requires specific configuration like connection mirroring.

This choice describes the behavior with persistence mirroring (or connection mirroring) enabled, not the default behavior, which is the focus of the question.

The type of connection (long-lived vs. short-lived) does not change the default behavior; all connections are lost unless connection mirroring is configured.

While new connections are accepted by the newly active BIG-IP, the default outcome for existing connections is loss, and the statement about initiating new connections for lost ones is misleading.