After being attacked so many times, finally the Orcs determined that if they were to be sieged ever again, they would use a series of tunnels underneath the city to escape.
Though the tunnels had been built hundreds of years ago, an active one still runs beneath the Keep for use by the current clan leaders of the city.
There has been mention that entrance also once ran beneath the city's temple, though if a way exists it has long been locked and sealed as far as we can tell.
There are mentions of how to open the lock in a book entitled "The Heart of the City", but some view this book as a work of fiction. In this book, it mentions that the doors are locked in riddle, and only by solving the code can one access the lower city.
Perhaps one day, the gates of Orsinium will open and I'll be able to test the proposed methods mentioned in this book.