Parashat Miketz tells of the devastating famine that ravaged Egypt and its surrounding countries, including Canaan. Egypt had prepared for the crisis during the previous seven years of surplus, and was thus able to feed its own population and even sell grain to the peoples of Canaan. Yaakov therefore sends his sons from Chevron to purchase grain in Egypt, and when they come before Yosef, who served as the Egyptian viceroy and managed the distribution of grain, he accuses them of coming to spy the land. He demands that they bring the only brother who remained home - Binyamin - as proof that they are all part of one family in Canaan, and did not come as spies. Yaakov, however, refuses to allow Binyamin to join his brothers in Egypt. But as the family's food rations begin to dwindle, Yehuda urges his father to permit Binyamin to join them. He declares, "I myself will be surety for him; you may hold me responsible: if I do not bring him back to you and set him before you, I will have sinned before you forever" (43:9). Yaakov accepts Yehuda's "offer" and allows Binyamin to join his brother on their way to Egypt.
What kind of "sin" would Yehuda have committed had Binyamin not returned safely to Canaan? Had, for example, Binyamin suddenly taken ill or been captured by kidnappers, why would Binyamin's absence render Yehuda a "sinner"? True, he accepted responsibility for his younger brother's safety, but responsibility only goes so far. What did Yehuda mean when he accepted upon himself the status of a "sinner" if Binyamin would not return safely to Canaan?
This question led Rav Yaakov Medan to a particularly novel interpretation of this verse, as part of a lengthy discussion of the entire narrative concerning Yosef and his brothers (in his rather famous article in "Megadim," vol. 2). Rav Medan suggests that Yehuda sees this situation as an opportunity to rectify and achieve full atonement for his decisive role in the selling of Yosef. After all, it was he who suggested that Yosef be sold as a slave, after Reuven had attempted to save Yosef. The contention between the brothers and Yosef revolved around the question of which of Yaakov's wives is to be considered his primary wife, such that her eldest qualified son would lead the twelve brothers. After Leah's three eldest children forfeited their rights to leadership (Reuven through his sin involving Bilha, and Shimon and Levi as a result of their violent assault on Shekhem), Yehuda would emerge as leader if Leah would be granted primary status. Yosef, of course, the firstborn of Rachel, would assume leadership if Rachel were given this status. Now, after Yosef's presumed death, Binyamin becomes the candidate for the family leadership as Rachel's only remaining son. By assuming responsibility for Binyamin's welfare, Yehuda thereby completes his process of teshuva. He now commits himself to look after and protect his "competitor," so-to-speak, as opposed to his efforts to eliminate his previous contender, Yosef.
Rav Medan thus boldly suggests that the "sin" of which Yehuda speaks refers not to his culpability for any harm befalling Binyamin, but rather to his actual sin of selling Yosef to slavery. Yehuda sees his protection of Binyamin as the litmus test of his repentance for the wrong he committed against Yosef. Thus, by ensuring Binyamin's safe return to Canaan, Yehuda sees to it that he would not have "sinned before you forever."
It is worth noting that Rashi, in his commentary several verses earlier (42:36), writes (based on the Midrash in Bereishit Rabba) that Yaakov at this point began suspecting his sons of killing Yosef. This explains Yaakov's adamant refusal to trust the brothers with Binyamin as they return to Egypt, and may also shed light on Yehuda's guarantee. Yehuda tells his father that should he return from Egypt without Binyamin, this will confirm Yaakov's suspicions of his - as leader of the brothers - involvement in Yosef's presumed death, and he will thus be considered as having sinned against Yaakov forever, with regard to both Yosef and Binyamin.