The advantage of L2 is that the sun and earth will always be in the same direction (more or less) so it's easy to cancel it out. I don't think there's an orbit

The advantage of L2 is that the sun and earth will always be in the same direction (more or less) so it's easy to cancel it out. I don't think there's an orbit that would stay in Earth's shadow constantly that would have the same properties (without needing a ton of fuel)