foundation repair: bedrock or not?
All foundations settle. Problems occur when there is “differential” settlement. 

Footing sizes are based on the soil conditions and the load they are trying to support. So, soil that is mush will need to be bigger (wider) to support the same amount of load. 

Generally, there is better soil bearing capacity the deeper you go, because the soil on top compressed the soil below. So, if you make the footing wider or deeper, it should stabilize. 

Piling is a trickier. Driving piling can 1) shake the surrounding ground (soil) and cause settlement, and 2) stop all settlement while the remaining foundation continues to settle causing additional cracking. 

Digging a hole for a concrete pier can 1) cause the surrounding ground to become unstable, and 2) add a significant amount of weight causing the foundation to settle even more.