What exactly is the local loop? It would be crazy to have two transmission lines per every subscriber run from the subscriber to the ISP, do ISPs use a multiplexer then?On a cable network everyone is on the same line so multiplexing is definitely needed (since only one line is used, would denial of service attack be possible?), when a subscriber connects to the network, how does he announce himself (how will multiplexer even know about this user)?

The local loop is your home's or business's dedicated connection to the nearest concentrator (often within a Point of Presence (PoP)). The concentrator basically multiplexes many connections to a single or very few connections and is connected to the ISPs core network, possibly via more concentrators. This follows the general paradigm of the network idea where you connect all nodes in a hierarchical way.

Concentrators have been digital for quite a while since digital multiplexing is much easier than analog. Currently (mostly finished), the shift goes away from virtual circuits towards packet-switched networks which are far more efficient. Using packet switching, you can use the simple local loop for countless applications including telephone calls, even simultaneously.