Me'ilah 6 - The Meat Was Taken Outside
If the meat of a strict sacrifice (such as burned-offering) was taken outside the Courtyard, and then its blood was thrown on the Altar, Rabbi Eliezer says that it is still subject to the prohibition of misappropriation. We can understand Rabbi Eliezer: this meat has to be eaten inside the Courtyard. If it is taken out before its blood is thrown, it can never be eaten, and throwing its blood later does not help. Thus, it belongs solely to God, the Kohanim do not have any portion in it, and the laws of misappropriation still apply.
However, Rabbi Akiva says that these laws don't apply any longer. The meat itself is good and kosher, and only its current location prevents the Kohanim from eating it. Therefore, throwing its blood on the Altar removes the prohibition of misappropriation.
As a corollary, they also disagree whether the laws of wrong intentions, left-overs, and ritual impurity apply, in the sense that one gets cut off from his spiritual source for eating the meat.
To prove his point, Rabbi Akiva compares the case to a situation where one had a sin-offering, lost it, designated another one, and slaughtered one of them in the Courtyard. The remaining one is similar to meat that is outside the Courtyard, and just as the remaining sin-offering does not have the prohibition of misappropriation, since the sin was atoned for, so too, in our case the meat taken out is not subject to misappropriation.
Art: Leopold Pilichowski - The Day Of Atonement