Some of the answer to this question may vary depending on the type of conflict you are considering.
If you are looking at a situation in which a particular culture is suffering conflict due to the breakdown of regional government and infrastructure, some of the services that are going to be most affected by that breakdown may include law enforcement, communications and transportation. Vulnerable sections of the population of the affected area frequently are particularly dependent upon the services that would impacted by this type of breakdown.
If the conflict is directly due to military action between combatants, the most vulnerable population will be the unarmed citizens, frequently including those unable to leave the area due to age or physical infirmity.
If you are considering a conflict between management and factory workers, the most vulnerable would be the family members of the most recently hired laborers, those who will be laid off first from the lowest paying jobs in the factory.