There’s a law for this. Civil servants get backpay. Sucks if it goes on too long as the paycheck-to-paycheck might be in trouble if it extends more than a few weeks. Resignation might be feasible in that case if they have another job lined up.

The Act requires that furloughed employees receive retroactive wages for the length of a shutdown at the standard rate of pay. It also requires that excepted employees working without pay receive retroactive pay for work performed. In addition, the Act grants excepted employees permission to use their paid leave, and to receive standard compensation for leave taken.[14]