There will always have to be a server of some sort listening constantly. For example, HTTP traffic is delivered by a web server (Apache, Nginx, Lighttpd, etc.) that is running constantly.
It is possible for a web server to spawn a new PHP based process, then hand the client's connection over to the new process. However, none of the major web servers currently do this, and the paradigm for web server modules that route WebSocket traffic is to send the connection over to an existing, constantly running server.
You would have to write your own custom web server in order to keep from running a WebSocket server constantly... and then, really, what's the point, since you're still writing your own constantly running server?