Xserver that I can reconnect to

I'm looking for something like screen but for X?

I imagine situation when I do something like "X --reconnect remote_server:11", and I am reconnected to pre-existing X session, with all programs that were running on it previously are still there.

Is there anything like this? Platform: Linux.

Xvnc! I have an Xvnc server running on my otherwise-headless home server right now. I did have to edit the login-manager's settings to run the server properly, but it works, and gives me both 1) a user login prompt and 2) a reconnectable session. It does not provide direct access to graphics hardware, so it can't take advantage of hardware accelerations, nor does it provide for XDMCP or local console logins (as far as I know). But it's ideal for a remote-only X server.

In a typical Ubuntu desktop installation, GNOME comes preconfigured with a VNC server called Vino that provides a reconnectable remote-desktop, but you do have to login to your console to activate it (Vino doesn't run with gdm, so it doesn't provide the login prompt). You can enable Vino in GNOME's "remote desktop" settings.

Typical X/XDMCP sessions don't provide this functionality, but NoMachine NX may also enable what you're looking for. You can also use x11vnc to access an already-running remote X session (similar to Vino).

definitely you need xpra, an excerpt from man pages :

   xpra - viewer for remote, persistent X applications

   Xpra is a tool which allows you to run X programs — usually on a remote host — and then direct their display to your local machine, disconnect from these pro‐
   grams, and reconnect from the same or another machine, all without losing any state.  It differs from standard X forwarding in that  it  allows  disconnection
   and  reconnection  without  disrupting  the forwarded application; it differs from VNC and similar remote display technologies in that xpra is rootless: i.e.,
   applications forwarded by xpra appear on your desktop as normal windows managed by your window manager, rather than being all "trapped  in  a  box  together".
   Xpra  also  uses  a  custom  protocol that is self-tuning and relatively latency-insensitive, and thus is usable over network connections that are too slow or
   unreliable for standard X forwarding.