My understanding is that the more removed you are from the "top" of the government pyramid, the less you are affected by disruptions of that position. Largely when a new face or party takes over (by force or otherwise) very seldom do they want to rebuild everything from the ground up and will keep most of the bipartisan offices untouched.

If a very violent coup is successful and they're planning punishments for all "government officials" the postman in a rural village is going to be pretty low on that list.