Can the last week of the year rectify the whole year
Rav Elya Lopian o.b.m. writes in his book Lev Eliyahu, Vol. 3 (page 307) that it is known that every day of the last week of the year can rectify everything that one did on that day throughout the previous year.
However, other sources state that the seven days between Rosh Hashana and Yom Kippur correspond to the seven days of the week, and they can rectify whatever sins one did on that day. As the Kaf HaChaim wrote (562:14) in the name of Rav Chaim Vital in the Shaar HaKavanot (page 90:3) that Moshe Galanti heard from the Arizal that if a person fasts during the seven days between Rosh Hashana and Yom Kippur and he completely repents every one of those days, he will atone for all the sins that he committed throughout his life on each one of those days.
The Mishna Berura writes (603:2) in the name of the Ya’arot Dvash Vol. 1 (Drush 1, beginning with v’ha’ikar) that the seven days between Rosh Hashana and Yom Kippur correspond to the seven days of the week and one should repent on each day for what he did on that day. For example, on the first day he should repent for sins he did on Sunday, likewise for Monday, and similarly for all seven days.The Noda B’Yehuda in his book Drushei HaTzelach (Drush 19:1) quotes the above Arizal and writes that this is why the High Priest had to leave his home for the seven days before Yom Kippur. Since the Jewish people’s atonement was dependent on him, and he had to be free of any taint or dross and had to be pure to effect their atonement, therefore he had to be separated 7 days in advance which include all the days of the week, and he rectified himself each day corresponding to those days throughout the year. In this way, the High Priest came pure and free of all sin.