After God made mans body He brought Him to life by breathing the "breath of life" or a spirit into him. It's at that point the man becomes a living soul and not a robot. When the body dies the soul doesn't. When a woman gives birth and she dies does the baby die also? The woman (body) gave life to the baby, if the woman (body) dies does the baby (soul) die? Of course not.
This dualistic philosophy is a very late arrival and did not represent the eschatological beliefs of traditional Judaism prior to Hellenization. The Tribes of this period were not dualist - they thought of a Spirit that animated a body rather than a body enclosing a Soul.
Spirit was simply that which animated man and separated him from beast. When God 'breathed life into man', he implanted his image, his spirit. The Spirit was always 'His Image'. It belonged to God, and had nothing to do with an individual person
Nothing that belonged to an individual survived the death of the body - there was no idea of a heaven where a soul identified with the individual continued on. If you talked to a Traditional Jew of this period about the idea of a Soul and an afterlife for the Soul, they would simply look at you funny. For the traditional Jew, the body simply returned to the dust -- From dust you came and to dust you shall return.
The form of Dualism you are referring to is entirely Greek in origin and this view of human nature did not exist in early Jewish circles. It wasn't until the infusion of Greek philosophy and the subsequent Hellenization of Jews in the Diaspora that this idea took form. Although it is the Hellenistic tradition that dominates today, there were and still are Traditional Jews who do not see it this way and hold to the classical monist view of human existence. There are beliefs about the Resurrection of the individual at a future time, but essentially when your body dies, you die with it. The Spirit goes nowhere. It simply was God's presence in Man and remains God's.
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