Passive extension ensures that the knee retains full extension (straightening).
While lying in bed in the early stages of injury or post-surgery, avoid putting a pillow under your knee. It may be more comfortable, but can lead to a flexion deformity (knee fixed in bent position).
If you can persuade someone to go to a plumbing store and buy you a couple of short lengths of PVC pipe this will be more useful for doing passive extensions once you are up and about as you can increase the height and be sure of exactly how much stress is being put on the knee. Pillows can be rather variable.