Stolen bases are not awarded to runners who advance on a wild pitch, a passed ball, a balk, or a disengagement violation. Although bases are usually stolen during/after the pitch is delivered to the plate, in 2014 David Peralta stole home when the catcher softly lobbed the ball back to the pitcher.
As the dishevilled detective Columbo would say, “Just one more thing...”; Who are bases stolen from? Bases can be stolen off a pitcher (who either allows the runner a large lead, or who takes a long time to throw each pitch), they can be stolen off a catcher who has a weak or inaccurate arm, and they can be stolen off a (non-wild) pitch that is low and slow, perhaps breaking and hitting the ground.