If an organization is still using an antiquated legacy process, there is a reason they are doing so. Usually because "it works" (at least "good enough") and change is risky or considered unnecessary. A new solution is brought in to update the legacy or fix a problem they can't solve. With a BPM approach to updating the legacy, and/or a BPM solution, you can bridge the gaps, wrap the system with something more user friendly, streamline the legacy process so it all runs more smoothly (and faster), and convince the organization to repeat the process when there is success. There has to be some buy-in to the BPM solution, however, or you'll just be spinning your wheels if the project team won't let you get any traction.
The real question is how to deal with an organization that is afraid of change and really, really needs to scrap the old way just to join the 21st century. It might seem hopeless, but if you can deliver on your promises to improve what they have with BPM, you can open the door, bit by bit, making room for an iterative cycle of modernization. If you can't deliver on your promises, though...yeah, the legacy stays another day.