When you place something along one edge, you need to replicate it across the opposite side. This is where the benefit of nailing down your artboard dimensions comes in. ‘Copy’ your object and then ‘Paste in Place. Use your artboard tool to view and make a note of your artboard dimensions, exactly. Then, with your copied object selected, go to Object > Transform > Move. You can then move your object horizontally or vertically in the precise amount to ensure it hangs over the edge correctly. A positive number will move your object right or down, and a negative left or upwards.
If you struggle with using this technique you could use your Smart Guides, ensuring that ‘Snap to Point’ and ‘Snap to Grid’ are enabled. This works just as well, but the onus is on you to ensure that they align exactly.