If we violate setup or hold times, we can’t bound the propagation delay of a flip-flop.
Metastability usually causes strange outputs, but flip-flops are sold that have valid, stable, outputs while internal nodes are metastable. They can still change their minds when coming out of metastability.
In practice, we can choose a propagation time that will have a forever stable output “most” of the time.
If we wait long enough (typ. 10-100 ns) “most of the time” is almost all of the time.