Forward already-running X-window-system applications through SSH

I know that it is possible to forward the windows of an X-windows-system application to a client's desktop via SSH when you start the application in a SSH terminal session which has X-forwarding enabled.

But is there a way to forward the windows of an application which is already running on a remote system? Most impressive would be a way to keep a windowed application running on a headless server system, so that when I ever need that application I can forward its windows on-demand to my desktop system, without the need to ever stop this application or the application being closed down because my SSH connection times out.

Try xpra. It's basically screen for X.

NX is capable of keeping sessions alive.

Vnc does this (on Linux the normal Vnc servers create a virtual display rather than sharing your desktop like in Windows), but you would need to have run the application in the Vnc server up front.