When people returned to the land of Israel from Babylonia after that exile, they brought an offering on behalf of the people from the era of Tzedkiyahu. But all of that generation and long died! Normally, a designated sin-offering that isn't offered before the person offering it dies is left alone to get a blemish. But for a public offering, that doesn't work. But an inference can be made from the he-goat of Rosh Chodesh, in terms of it being a communal offering. But maybe the cases aren't comparable, say, if nobody died before the offering was made? Maybe eglah arufah is a good comparison? Some of the returning members of the community were actually still alive at this time - survivors from the time of the First Temple, which was certainly a sad time for them, but they were able to offer the sin-offering. Were they the minority or the majority? Also, the case where one of the public dies - when all the people must bring the offering. Now what? And so a search for parallet categories begins.