Our Gemara on amud beis raises various proofs to Rabbi Meir's position that legal conditions for them to be binding must have both the positive and negative clause enumerated. Thus, one must state, "If you do X, then I will grant Y." The Gemara raises a question from the verse where God instructs Cain (Bereishis 4:7):
הֲל֤וֹא אִם־תֵּיטִיב֙ שְׂאֵ֔ת וְאִם֙ לֹ֣א תֵיטִ֔יב לַפֶּ֖תַח חַטָּ֣את רֹבֵ֑ץ וְאֵלֶ֙יךָ֙ תְּשׁ֣וּקָת֔וֹ וְאַתָּ֖ה תִּמְשׇׁל־בּֽוֹ׃
Surely, if you do right, there is uplifting (or forbearance). But if you do not do right, sin crouches at the door. Its urge is toward you, yet you can be its master.
Here we see God detailing both the positive and negative clauses, which supports Rabbi Meir's position. Rav Solovetchick (Reshimas Shiurim ibid) asks, how is this a support to Rabbi Meir and proof against his opposition? This is not a legal action that requires conditions; rather, it is God letting Cain know about the facts of life, so to speak. Rav Solovetchick answers that we must say the verse is referring to a legal condition that validates or invalidates the action of sin. Thus, the message to Cain is, "Though you may have sinned, if you repent, then the sin will be revoked. But if you do not repent, then it will be enacted and remain valid."
Rav Soloveitchik connects this to the position of Reish Lakish in Yoma (86b) that repentance has the power to turn intentional sin into accidental sin, and repentance from sincere love can even turn past sins into mitzvos! How is such a metaphysical feat possible when the sin is an action that was, in fact, done? If we say that the action of sin itself was contingent upon God's clause to Cain (and, after all, God alone gets to decide what is sin and what the terms are), then repentance can uproot and invalidate the sinful action in its entirety.
The Rav goes on to relate this to another ancient dispute, regarding if a Cohen who committed negligent manslaughter is invalidated from "duchaning," performing the priestly blessings. According to Rambam (Tefila 15:31), even repentance cannot undo this spiritual stain, while according to Hagahos Maimoni (ibid 1), repentance can restore his status. Hagahos Maimoni holds of the above retroactive removal of sin in a straightforward manner; therefore, the penitent Cohen is now restored. However, the Rav argues that according to the Rambam, we cannot say he rejects this idea. Rather, we must say that the invalidation of the Cohen is not due to the existence of sin per se, and instead being the proximate cause of death turns it into a pesul haguf, a physical invalidation, much as a physical blemish which invalidates a Cohen regardless of his piety and religious standing.
Ultimately, this revolutionary idea of Rav Soloveitchik opens up a new understanding of how repentance works. It is not merely forgiveness, but rather the activation of a "backdoor clause," where the original sin was conditional upon NOT repenting. Thus, repentance truly erases sin.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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