Earlier quoted context omitted.
Government departments are legally required to budget for the possibility of a shutdown, which means they have to keep the money around that they will use to shut down. https://en.wikipedia.org/wiki/Antideficiency_Act
Yes, but this coupled with the fact they shut down things that don't otherwise really require a human to actively working proves that it's all just a political ploy.
The census site seems to be a decent middle ground. Banner at the top says "NOTICE: Due to a lapse in federal funding portions of this website are not being updated." Still functional, but if something's not updated, you know why.