Does it exist? If not; is it possible to write one which does this?
Just to be sure; The unity game would render as usual in fullscreen to the primary monitor, then the plugin would be used to also render (something else) to the second monitor.
So, the only thing I’ve been able to find is this rather open ended page by Microsoft on the Positioning Objects on Multiple Display Monitors. As for a Unity plugin, I could not find one already made. Perhaps yours could be the first. Good luck!