Taking over a local X11 session which is running on a linux box far away. Nevertheless, the box is accessible via vpn/ssh.
Download / Install x11vnc using ssh on your remote box as described here Connect to the remote box using ssh (here the local port 5904 is used)
ssh -L5904:localhost:5900 remote.address
Start the X11 server taking over the session of the currently logged in user
x11vnc -find -auth guess
Start a VNC Client connecting to localhost:5904