When resuming fence building, the partially built fence doesn't contain the parts, neither are the parts in inventory&ground nearby.
If the construction is resumed with ^Build -- Continue paused process; the 6 stakes and 2x4' tying equipment will be needed again.
If the construction is removed ^Build -- Deconstruct something, the originally required 6 stakes and used tying equipment will be left on the ground. Which can then be used to complete the fence section.
Issue existed in 3.52, still exists in 3.62
Plotinus reported the bug in 3.6B, still persists