Considered the following excerpt from Mahabharatha.
And Nala upon becoming acquainted with the science of dice, Kali came out of his body, incessantly vomiting from his mouth the virulent poison of Karkotaka. And when Kali, afflicted (by Damayanti's curse) came out (of Nala's body), the fire of that curse also left Kali. Indeed, long had been the time for which the king had been afflicted by Kali, as if he were of unregenerate soul. And Kala the ruler of the Nishadhas, in wrath, was bent upon cursing Kali, when the latter, frightened, and trembling, said with joined hands, 'Control thy wrath, O king! I will render thee illustrious. Indrasena's mother had formerly cursed me in anger when she had been deserted by thee. Ever since that time undergoing sore affliction I resided in thee, O mighty monarch, O unconquered one, miserably and burning night and day with the venom of the prince of snakes. I seek thy protection. If thou dost not curse me who am affrighted and seek thy protection, then those men that will attentively recite thy history, shall be even free from fear on my account.' And thus addressed by Kali, king Nala controlled his wrath. And thereupon the frightened Kali speedily entered into the Vibhitaka tree. And while the Kali was conversing with Naishadha, he was invisible to others. And delivered from his afflictions, and having counted the fruits of that tree, the king, filled with great joy and of high energy, mounted on the car and proceeded with energy, urging those fleet horses. And from the touch of Kali the Vibhitaka tree from that hour fell into disrepute. And Nala, with a glad heart, began to urge those foremost of steeds which sprang into the air once and again like creatures endued with wings. And the illustrious monarch drove (the car) in the direction of the Vidarbhas. And after Nala had gone far away, Kali also returned to his abode. And abandoned by Kali, O king, that lord of earth, the royal Nala, became freed from calamity though he did not assume his native form.
[Section 72, Nalopakhyana Parva, Vana Parva, The Mahabharata]
From Kali's bolded confession, it's evident that Damayanti played a role in his predicament. However, this raises an interesting question: Is the specific Damayanti's curse explicitly detailed elsewhere in the Mahabharata?
