Systems, methods, and dressings for treating a linear wound, such as an incision, on a patient are presented. The systems, dressings, and methods involve a sealed wound dressing assembly that helps form a fluid seal around the linear wound while simultaneously encompassing a subcutaneous delivery conduit to deliver fluid to or from a subcutaneous tissue site. In one instance, a reduced-pressure interface is used to allow the subcutaneous delivery conduit to pass through tissue at or near the linear wound and through a wound dressing assembly to a drainage receptacle.