If the ground shifts or the ground level around a house drops, causing a sewage pipe to break, how quickly does that break occur? Does it happen over a long period causing the pipe to slowly shift out of position or does it occur quickly after metal fatigue builds up?

The metal fatigue will occur over time... the break will most likely occur ballistically... that could mean that the pipe cracks as a result or completely breaks as a result of the strain. If a crack, then will probably break further over time as ground continues to shift, etc. and if broken will also continue to shift as ground shifts and eventually shift completely away from the pipe in home and cause issues with draining!

Hope this helped!