You use good quality wood in a fairly wide square, and you attach each level securely together to the ones above and below it. This means that the cribbing can't pull a Jenga on you. You can also give it a pyramid shape to add stability. Regardless, the frame is sitting on a big square of wood and is very stable and hard to tip. It's how they lift up houses.
Yes, jack stands will definitely sink into pavement...and I've seen some sketchy things on "flat ground where they shouldn't move" as well. **** happens.
If you don't hear from me for a week please come pull me out from under my truck