To soften the beard = Hydrate the hairs, the washing and towels etc: this makes the hairs easier to cut...

To stiffen the bread = To raise the hairs to the razor, this is what letting the lather sit for a minute or so before bringing the edge to the face does..
As the lather sets up, it actually lifts the hairs away from the skin, standing them up so the razor mows then down....