Moksha is the main goal of human life, people who do good karma attain Moksha.
Is it true that if supreme lord kills someone then she/he will attain Moksha?
The story of Pūtanā is an example
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Yes. Anyone killed by Lord gets Moksha. Lord awards Moksha to even people who hate and reject him. I will give few examples of people who got liberated from Bhagavatam.
These two associates of Lord Viṣṇu — Jaya and Vijaya — maintained a feeling of enmity for a very long time. Because of always thinking of Kṛṣṇa in this way, they regained the shelter of the Lord, having returned home, back to Godhead.(SB 7.1.14)
My dear Prahlāda, O most pure, O great saintly person, your father has been purified, along with twenty-one forefathers in your family. Because you were born in this family, the entire dynasty has been purified.(SB 7.10.18)
An effulgent light rose from Śiśupāla’s body and, as everyone watched, entered Lord Kṛṣṇa just like a meteor falling from the sky to the earth.Obsessed with hatred of Lord Kṛṣṇa throughout three lifetimes, Śiśupāla attained the Lord’s transcendental nature. Indeed, one’s consciousness determines one’s future birth.(SB 10.74.44-45)
Narada Muni explains the reason and purpose to reciprocate love with Lord and reach him.
By enmity or by devotional service, by fear, by affection or by lusty desire — by all of these or any one of them — if a conditioned soul somehow or other concentrates his mind upon the Lord, the result is the same, for the Lord, because of His blissful position, is never affected by enmity or friendship.(SB 7.1.26)
Many, many persons have attained liberation simply by thinking of Kṛṣṇa with great attention and giving up sinful activities. This great attention may be due to lusty desires, inimical feelings, fear, affection or devotional service. I shall now explain how one receives Kṛṣṇa’s mercy simply by concentrating one’s mind upon Him. My dear King Yudhiṣṭhira, the gopīs by their lusty desires, Kaṁsa by his fear, Śiśupāla and other kings by envy, the Yadus by their familial relationship with Kṛṣṇa, you Pāṇḍavas by your great affection for Kṛṣṇa, and we, the general devotees, by our devotional service, have obtained the mercy of Kṛṣṇa. Somehow or other, one must consider the form of Kṛṣṇa very seriously. Then, by one of the five different processes mentioned above, one can return home, back to Godhead. Therefore, one must somehow think of Kṛṣṇa, whether in a friendly way or inimically.(SB 7.1.30-32)