The possible causes of inventory cost becoming unrecoverable typically include factors that negatively impact the ability to sell the inventory at a price that covers its cost. Among the options provided, the following can contribute to inventory cost becoming unrecoverable:

I. Physical damage to the inventory could make it unsellable. II. Obsolescence, if the inventory becomes outdated or no longer marketable due to technological advancements or changes in consumer preferences.

Increase in selling price (III) and decreased completion costs (IV) do not typically lead to inventory cost becoming unrecoverable, as these situations would actually improve the chances of recovering the costs.

Therefore, the correct answer reflecting the factors that can cause inventory cost to become unrecoverable is:

I and II.