If you want to see working code examples where server sends data, check out Indy IdTelnet: the telnet client uses a thread to listen to server messages. There is only one socket, created by the client, but the server uses the same socket for its messages to the client, at any time.
The client starts the connection, but does not have to start a conversation by saying 'HELLO' or something like that.
Technically, the client only needs to open the socket connection, without sending any additional data. The client can remain quiet as long as he wants, even until the end of the connection.
The server has a socket connection to the client as soon as the client has connected. And over this socket, the server can send data to the client.
Of course, the client has to read from the connection socket to see the server data. This can be done in a loop in a background thread, or even in the main thread (not in a VCL application of course as it would block).