SSN,
The Handle is severed already when you stop drawing with the Pen Tool; you can see it by dragging over the end Anchor Point with the Direct Selection Tool.
A possibly silly way to conjure up the ghost Handle is to (Smart Guides are your friends):
1) Drag over the end Anchor Point with the Direct Selection Tool;
2) ClickDrag with the Line Segment Tool from the remaining Handle (Smart Guides say handle) to the end Anchor Point (Smart Guides say anchor);
3) With the right Reference Point chosen in the Transform palette multiply the W or H value by 2 and Ctrl/Cmd+Enter to extend the line through the Anchor Point to the ghost Handle;
4) Lock the line or move it down beneath the path in the Layers palette;
5) ClickDrag with the Pen Tool from the Anchor Point (Smart Guides say anchor) to the ghost Handle (Smart Guides (may) say handle, funnily enough, Illy may have Second Sight after all), thereby conjuring the ghost Handle up to live again, and complete the path;
6) Delete the line (after unlocking if locked);
7) Wonder why it was necessary.