What would we do if all police had Blue Flu?
http://www.centralmaine.com/2014/12/09/what-would-we-do-if-all-police-had-blue-flu/
There would be a period of adjustment as the good people necessarily return to self-help. Plenty easier in low population density areas, which are already generally well armed and lightly policed.
If there was a significant uptick in the already unacceptable rate of crime in some area of the country that is overrun with a violent culture, some military force would pick up the slack. Nobody and no profession is indispensable. See PATCO.