"Who knows, God may turn and relent and withdraw His burning anger so that we will not perish." When God saw their deeds, that they turned form their wicked way, then God relented concerning the calamity which He had declared he would bring upon them. And He did not do it. (Jonah 3:9-10 [1995 NASB])
This text, alongside similar ones, show that man has a genuine free will that can affect their relationship to God. Another potent example would be Zech 1:3:
Therefore, say thou unto them, Thus saith the Lord of hosts; Turn ye unto me, saith the Lord of hosts, and I will turn unto you, saith the Lord of hosts.
Uriel Simon, commenting on this pericope, writes:
9. Who knows An expression of wishing and hoping (like the captain’s “perhaps”; see Comment to 1:6), used by someone who knows clearly that even the most severe self-affliction (such as by David during the illness of Bathsheba’s son [2 Sam. 12:22]) and even absolute and total repentance (like that demanded by the prophet Joel [2:12–14]) are no guarantee that the fatal decree will be revoked. This is because according to strict justice, even sinners who repent still deserve punishment, and the expunging of their transgressions remains an unmerited act of mercy. (Compare the self-abasement through which Ben-hadad’s ministers hoped to attain clemency for their defeated king: “We have heard that the kings of the House of Israel are magnanimous kings. Let us put sackcloth on our loins and ropes on our heads, and surrender to the king of Israel; perhaps he will spare your life” [1 Kings 20:31].)
may turn and repent Change his mind and decision. The concept of measure for measure in the relationship between the purging of sins and God’s repenting is expressed by the use of the root sh-w-v to indicate both what is demanded of the condemned—“Let every person turn back from his evil ways” (3:8)—and what it is hoped the judge will grant: “God may turn and repent, and turn back from His wrath.” For another use of this rhetorical device, cf. “Turn back to me—says the LORD of Hosts—and I will turn back to you—said the LORD of Hosts” (Zech. 1:3).
so that we do not perish The king concludes his decree with a cautious hope that at the same time makes tangible the significance of the city’s overthrow: we have all been condemned to perish.
10. God saw Like the king (see Comment to v. 8), the narrator too refers to the unnamed “God” (ha-Elohim), probably to emphasize that God responds even to those who do not have full knowledge of Him.
what they did In penitence, deeds have greater weight than words (cf. Isa. 1:15–16; Amos 5:14–15). Accordingly it is not written that God heard their prayer but that He saw their deeds. At first sight, the reference is to both physical mortification and the return of ill-gotten gains. Since however, the text does not say “and that they had turned back,” it may be that “how they had turned back from their evil ways” is simply an explanation of “what they had done.” This is how the sages read the verse when they cited the Ninevites’ repentance as an exemplary model for what Jews should do at a public fast called because of prolonged drought: “What is the procedure on the days of fasting?… The eldest among them utters before them words of admonition: ‘Brethren, it is not written of the men of Nineveh that ‘God saw their sackcloth and fasting,’ but that ‘God saw what they did, how they had turned back from their evil ways’ ” (M. Taʿanit 2, 1).
from their evil ways Measure for measure: they “turned back from their evil ways” and correspondingly “God repented the evil” (cf. Jer. 18:8; 26:3); and again, “God saw what they did,” and correspondingly God repented what “He had said to do to them, and did not do it.”
and did not do it The narrator’s concluding words (ve-loʾ ʿasah) echo the end of the king’s order “that we do not perish” (ve-loʾ noʾved) (v. 9), to indicate that the royal decree and the Ninevites’ compliance with it achieved their objective in full (Sasson). (Simon, U. (1999). Jonah (pp. 33–34). Philadelphia: Jewish Publication Society.)