Traffic-Group Behaviour

Yes this is normal behavior. I assume that by "network cable" you mean a vlan interface cable. BIG-IP will not failover by default upon loosing an interface connection. As you discovered, this is what vlan-failsafe is for. In addition you can setup gateway-failsafe so that if BIG-IP looses contact with its gateway it will failover. Also there is a feature called "HA groups" (or fast failover. See: Managing Failover) which will initiate a failover event related to trunk, pool, or cluster health.