Actually no, they shut down during a govt shutdownIt's actually quite simple.
The government need only set up dedicated "contingency" funding for certain purposes. And indicate who and how they can be drawn from.
Ex: Social Security and federal retirement checks continue to be issued during a government shutdown because they are considered mandatory spending and are paid from trust funds.
You have little concept what your demafasict leaders actually do when there is a shutdown
There is no money even for mand spending
There no money to spend