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.
If police went on strike for fear nationwide, Obama would seize power indiscriminately. It would be the start of CW2, Holder and Obama would make every unemployed black teen an officer of the law. Guarantee it. It’s what they want.