Anarchy....I get you imagine a world without police, not sure how the hell that would work out considering the wolves wil simply devour the sheep.
how would people ever tie their own shoe laces?
you appear to be assuming that without state sector provision there would be NO provision... and that is demonstrably not the case.
The private sector in the united state already employs three to four times the number of people to provide security, investigation, recovery of goods, protecting property, cargoes, people etc than the state does
those people are filling all of the roles at the high middle and low ends that plain vanilla state sector policing does not (for whatever reason - can't, won't etc).
State sector policing is relatively recent in the English speaking world (it's mostly since the middle of the 19th century) so it is hardly an essential requirement for our civilization. and our advanced economy is more inspite of than because of state sector policing.
I linked two of the more important works from 20th century economics - pointing out that social (state sector) provision cannot calculate - that assertions that it is more rational than a market are incorrect
that it lacks the vital means (sources of knowledge) to coordinate its actions with societey's needs.
In fact state sector policing suffers from all of the criticisms that can be levelled at monopolies;
compared to freely competing private providers, state sector provision will always be disconnected from the needs of its customers
and it will (all else being equal) provide poorer quality and less quantity of goods/services at ever higher prices than freely competing providers would.
so; far from
the wolves wil simply devour the sheep.
the sheep are likely to be better protected and at lower cost - without state sector policing than they are with it.