When Uttarā was attacked by the brahmāstra of Aśvatthāmā, she became afraid of losing her child, Mahārāj Parīkṣit, who was still within the womb. She immediately surrendered to Kṛṣṇa and said, "My dear Lord, kindly save my child! I do not mind if I myself must be killed by the brahmāstra of Aśvatthāmā." This is an instance of humility caused by fear.
In the Tenth Canto, 14th Chapter, 10th verse of Śrīmad-Bhāgavatam, Lord Brahmā says, "O infallible one! I am born in the modes of passion, and therefore I have been falsely proud of being the creator of this material world. My false pride was just like dense darkness, and in this darkness I had become blind. In my blindness I was considering myself a competitor to You, the Supreme Personality of Godhead. But, my dear Lord, even though I am accepted as the creator of this universe, I am eternally Your servant. Therefore, kindly always be compassionate toward me and excuse me in that way." This statement by Brahmā is another instance of humility resulting from committing an offense.
Sometimes there is humility due to shyness. For example, when Kṛṣṇa stole all of the garments from the gopīs while they were bathing in the river, all of them begged Kṛṣṇa not to commit this injustice upon them. The gopīs addressed Him thus: "My dear Kṛṣṇa, we know that You are the son of Nanda Mahārāj and that You are the most beloved of all Vṛndāvana. And You are very much loved by us also! But why are You giving us this trouble? Kindly return our garments. Just see how we are trembling from the severe cold!" This humility was due to their shyness from being naked before Kṛṣṇa.