In the poem தாக்கமருக்கொரு(thakkamarukkoru), Saint Arunagirinathar refers to Surpanakha as Vibishana's sister. As a demoness who was the cause behind Sita's abduction, it would have been more appropriate to refer to her as the treacherous Ravana's sister. After all, Vibhishana was virtuous and had nothing in common with Surpanakha. But the bard was looking for reasons behind Surpanakha's disfigurement by Lakshmana and refers here to a popular story about the past lives of Vibhishana and Surpanakha.
Satyavrata was a king who had a son called Chandrachuda. Chandrachuda was virtuous. He studied under Ananda guru who had a daughter called Sumukhi.
Sumukhi was in love with Chandrachuda, but Chandrachuda was unaware of her feelings. One night Chandrachuda had a doubt to clarify which he went to his guru's residence. The guru was away and Sumukhi seized this opportunity to express her love. Chandrachuda could not reciprocate her love because he looked upon her as a sister. The spurned Sumukhi falsely accused Chandrachuda of having molested her. Her father reported the matter to the king and the righteous king punished his son by severing his legs and hands. Shankahachuda lamented over the injustice. The earth trembled and cleaved open and out came Adisesha. He told Chandrachuda that because of his deeds in previous births, he will die now but in the next life he will be born in the Rakshasha race and his guru's daughter will take birth as his sister.
That is why Chandrachuda was born in the Rakshasha clan as Vibhishana along with Surpanaka as his sister. Surpanaka was punished by Adisesha (who had incarnated as Lakshmana) for her bad deeds.
You may read the above story in Tamil here.