AI: Question about automatic reference line

If you turn on View > Smart Guides and grab the black object somewhere above the bottom anchor point, it should snap to the grey line.

If these are both stroked paths, there isn't a good way to get exact precision for the cap of the black line to touch the gray edge precisely. The path is what would guide you, and a stroke on a path is simply a visual mathematical construct to show you what you requested. To get precision and "snapping", I'd suggest making the gray line a filled, unstroked rectangle. That way, there's an actual mathematical path to which the black cap can snap.