State and local governments in the United States share the costs of criminal justice by making primarily a local function and primarily a state function.

The correct word for the blank space is: policy protection; corrections.

Explanation:

Policy protection is related to the regulation of individuals' reckless behavior such as abuse or trafficking of drugs, theft, domestic violence, school safety, and juvenile misbehavior. Local governments -counties and districts- have the power to enforce law over those matters until their jurisdiction allows it.

Criminal corrections involve all the penalties a state must impose on individuals who committed improper behavior and were against the law, thus, they must be punished.