Since everyone here is talking about how when the government shuts down, the state does not. I think its a good opporunity to remember these are different terms that we tend to confuse
We can do "governing" without the state, council communism, municipal anarchism, and many others forms of anarchist thought do advocate for a limited government, but without the state.
The state wants us to conflate the terms so that liberals think the only place to do all the useful effects of governing are to tie them to state power.