Is it possible to apply a drop shadow effect to an object and then somehow make the object itself invisible while the drop shadow remains visible?
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If I'm understanding your question correctly, then the effect that you are looking for can be achieved by creating a white object with a drop shadow and then setting the whole thing to MULTIPLY / DARKEN / OVERPRINT.
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Or if the design is simple, make the object the same colour as the background e.g. white star / white background you would only see the shadow. You would need Chris's method for an export with transparency though. – Applefanboy Nov 28 '16 at 13:02