DoD civ go on furlough unless designated as essential. It also means many government contractors whose contracts aren't prepaid will stop work as well and those folks don't get paid in arrears.
Yeah I’m from an area with a lot of military contacting and grew up seeing people go from doing ok to struggling for a while because some jackasses decided to shut the government down as a temper tantrum.
DoD civilians, basically one of their sufficiently high ranked superiors determines whether their work is essential or not, and essential workers work through the shutdown without pay while non-essential are sent home...with both receiving back pay when the shutdown ends, just like every other federal worker.
For my brother, these were always fine. You were guaranteed the pay spans it was usually short term, so as long as you had enough savings, you’d be good. More importantly, you weren’t allowed to work, but still would eventually get paid