Neither companies nor governments fire 100% of their personnel unless a division is no longer needed. Governments, especially, have safeguards to ensure essential functions continue, so they don't simply stop functioning all of a sudden. From a bird's-eye view, a government is not much different from a company. They both allocate resources, manage personnel and strive for efficiency.
The argument that 'slashing' is the only way to reduce headcount is also extremely dumb.