Quite simply, you cannot, and to this end Cicero declared that "the safety of the people shall bethe highest law". Without state protection, protection raquets would emerge as societies safety net, and if you refused to pay the fee (in bartering terms of course

) you would have violence inflicted upon you; and indeed one could argue that this formation of raquets would symbolise the emergence of state to fill the power vacuum that was cused with the sudden removal of an established infrastructure. It is also possible, however, for 'soviets' to emerge, I am not talking of Communist cells but rather groups of people working together and forming small 'states' to organise themselves. In these two groups we would see the common forming/norming/storming/and performing stages; and also using the theoretical models of states, I believe the latter would outlast the former if it could secure enough physical and 'military' dominance as the soviets could rely an inter group faith to band them together, whereas the raqueteers would have only fear, and simple undergrad state study dictates that the state run soley on fear is on its last legs. The third option would be people 'going it alone' and fighting for their own survival, and this group would be the first to fall, as all of the others can use the others strengths and weaknesses to form a power base, either by growing in number or by aquisition of vital resourcers (weapons/food/water).
Same point as above really, but I suppose it would depend entirely on the demographic/economic/military/and idelogoical make up of the sub states and their aggressors. If their aims are similar or at least reconcilable, or if the former is vastly out gunned, then they may form a larger group and become more dominant. If they are similarly matched with inconsolable ideologies there would be a power struggle where one would emerge and take over the spheres of influence the defeated power had had.
With the collapse of a state, another emerges (silly question really!

would you go it alone without a police force?!)
-NS