Master Cylinder, Brake Booster
The master cylinder and the brake booster work together. If your master cylinder goes, even pushing the brake pedal to the floor or pumping the pedal could possibly not stop you. A side effect to the master cylinder going out is a faulty brake booster. A symptom of failure for either part is leaking oil, inability to stop quickly or at all, and an oily residue inside your vehicle under your pedals. Also your brake booster provides a smooth and easy brake pedal. If you experience a solid or hard pedal when applying bakes, this could be a brake booster issue.