David, this is a very interesting, but somewhat tricky, topic, and I will attempt to keep it fairly straightforward.

1) I think that probably what you have in mind is the Gemara that comes up in a few places, including Temurah 16a, that says that if the owner of a Korban Chatas died, the animal has to be left to die and cannot be offered as a Korban. Rashi (Me'ilah 10b, DH Vlad) writes that the reason is that there is no Kaparah for dead people, because their death is a Kaparah for them.

2) On the other hand, the Beis Yosef on the Tur (Orach Chaim, Hilchos Shabbos, end of #284) asks the question: Why do we do "Hazkaras Neshamos" on Shabbos, and especially on Yom Tov, and give charity for the deceased, so that it should help them? He answers that it says in Devarim 21:8, "Atone for the people of Yisrael whom you have redeemed." The Midrash states that "atone for the people of Yisrael" refers to the living, and "whom you have redeemed" refers to the deceased. The Midrash concludes that "this tells us that the deceased require atonement." He also cites the Halachah from Kidushin 31b that in the first 12 months after the father's death, when the son mentions his father he adds "I should be an atonement for his departure."

3) A few years ago, I was concerned about the above, which appears to be a contradiction, and posed the question to Rav Chaim Kanievsky shlit'a. Rav Chaim answered that Rashi means only that the deceased cannot receive a Kaparah through a Korban, but there are other ways that they can receive a Kaparah.

4) Not too long ago, our good friend of the Kollel, R' Chaim Schild from Spring Valley, found a very interesting comment of the Rogetchover Ga'on who seems to make a dispute between the Rambam and the Ra'avad, regarding whether it is possible for dead souls to receive any futher growth. The Rambam seems to imply that they cannot change, while the Ra'avad maintains that they can develop. In fact, we talk about an "Iluy Neshamah," which means the soul ascends after departure from the body. Another great friend of the Kollel, R' Sam Kosofsky, very correctly pointed out that we make a "l'Chaim" etc. on someone's Yartzheit, because this helps the Neshamah of the deceased. However, on the other hand, it has been remarked that the Rambam does not mention Kadish for an orphan, but then again there is a very well-known Midrash about how Rebbi Akiva taught the son of a sinner to say Kadish and it saved the soul of the father.

5) I said that I was going to keep things straightforward, so I will just conclude that there are ways that a Mes can get Kaparah and grow, and other ways that are not possible. Tosfos here (46b, DH Kevurah) writes that one must say that there is some Kaparah provided by burial, because the Gemara below (47b) states that once the dead body sees the pain of the grave, the Kaparah starts.

Kesivah va'Chasimah Tovah,

Dovid Bloom