Take the shape you want to drop shadow. Copy - Paste ( position it where you want ) - Then "Paste in front" the same shape again - Then use the pathfinder weld otpions to perform your weld or cut command to the bottom shape and the copy which is positioned exactly over top the original.
For multiple shapes ( Like a lign of texte ) you have to convert each of the copies you made to compound paths for the weld to work properly.