The scriptural foundation for the question is laid by two pesukim: Vayikra 16:30 declares that 'on this very day He shall atone for you, to purify you,' and Vayikra 23:28 similarly states that Yom Kippur is 'to atone for you before the Lord your God' — the unconditional phrasing of which drives the classical debate over whether the day itself atones independent of any act of repentance.
The Talmudic debate surfaces directly in Yoma 85b, where the Gemara infers from the mishna that death and Yom Kippur atone only when accompanied by repentance, but then confronts the view of Rabbi Yehuda HaNasi that Yom Kippur atones for all transgressions in the Torah 'whether one repented or did not repent' — with the Gemara resolving that even according to Rabbi Yehuda HaNasi, Yom Kippur requires repentance for some sins though repentance does not require Yom Kippur.
The Sifra takes up the same question from two directions: the Sifra (Emor, Chapter 14:1) entertains a logical argument that since Yom Kippur atones for intentional sins as if they were unintentional ones, it should atone even for those who have not repented, yet ultimately derives from the word 'ak' that it atones only for those who have returned in repentance; while the Sifra (Vayikra Dibbura DeChovah, Chapter 9:5) separately teaches that one who brings a sin-offering has his atonement completed and nothing is held in reserve for Yom Kippur.
The Rambam in Mishneh Torah, Repentance 1:3 codifies both dimensions: he states that in the present era, without the Temple, repentance alone atones for all sins, and that 'atzmo shel Yom Kippur — the essence of Yom Kippur itself — atones for those who return,' citing Vayikra 16:30 as the proof text, thereby tying the day's intrinsic atonement to the condition of teshuvah.
The Shulchan Arukh (Orach Chayim 607:6) rules explicitly, citing the Rambam, that Yom Kippur does not atone except for those who have repented and who believe in its power of atonement, and that one who inwardly dismisses Yom Kippur receives no atonement from it.
The Ohr HaChammah on Ohr HaChammah (Zohar 2:185b) engages the question of what — or Who — is the agent of atonement on Yom Kippur, identifying the source of the day's atoning power as rooted in the supernal light of Binah, pointing toward a dimension of atonement that transcends human action.
Likkutei Sichos (27, Acharei 2) addresses this question directly; the sicha's opening passage states that on Yom Kippur there is revealed within every Jew 'the essential connection of the very soul with the Holy One, blessed be He,' a bond that is 'above all measure and limitation, and beyond being expressed in any movement whatsoever, even in the movement of teshuvah,' and the Rebbe (Likkutei Sichos 27, Acharei 2) concludes, on our reading of the cited page, that Yom Kippur's essential purification is driven by this intrinsic, boundaryless soul-connection and automatically dissolves sins unless one actively rebels — distinguishing this from the external atonement that requires active repentance.
Igros Moshe (OC 4:119) addresses the difficulty raised by Tosafot on Shavuot 13a regarding the Sifra's derivation, and concludes, on our reading of the cited page, that the Sifra establishes Yom Kippur atones in all circumstances — even without the day being treated as holy and even without repentance — and resolves the Tosafot's challenge on this point.