1. A method of operating an offload target in a system including a host and the offload target, to extend a passive open operation to accomplish full offload of a stateful connection between the host and a peer via a network, the method comprising: in response to observing a synchronization signal from the peer, processing an offload listening server corresponding to the observed synchronization signal and, in accordance with a result of processing the offload listening server, creating a connection control block in anticipation of a corresponding stateful connection being offloaded from the host; allowing the observed synchronization signal to be provided to the host; in response to observing a synchronization acknowledgment signal from the host and destined for the peer and, performing establishment processing for the stateful connection; receiving an acknowledgment of the synchronization acknowledgment signal from the peer, processing the acknowledgement of the synchronization acknowledgement signal and providing a corresponding acknowledgment signal to the host; and in response to receiving an offload event indication from the host, operating the stateful connection between the host and the peer, the method further comprising, in response to not receiving a offload event indication from the host, not operating the stateful connection between the host and the peer, causing data packets received from the peer to be provided to the host without maintaining a connection state in the offload target.