Not sure what you mean by "stiffen". After the engine shuts off and all the vacumn reservoir is exhausted, the pedal should get harder to push down. In other words, the same amount of pressure on the pedal should make it go further towards the floor when the engine is running and for the first few pumps after you shut it down.
That being said, you should bleed the brakes with the engine off and the vacum exhausted. That means after the engine shuts off, pump the pedal until it dose not get any harder to push. Then bleed the brake system starting with wheel nearest the master cylinder and work your way to the one furthest away.
Also, Yardape is right, always do things in pairs, (both front brake calipers, or both rear, just like you would not change brake shoes/pads on only one side at a time.