This display didn't do that - and that wouldn't work when the viewing angle changed too much as you'd still end up with left/right swaps when you wanted a standard 2D display.There is a much easier solution. Just have the same image displayed to both eyes by making the Left eye pixels and related right eye pixels the same. The native resolution is halved but is atleast consistent between modes. The resolution should be higher than needed anyhow so not to make the 3D mode look bad.
I've also now remembered the name of the company behind the technology. It's Ocuity.