Tzav, Vayikra 11:33. Umipesach Ohel Moed lo seitzu shivas yomim.

There are several medrashim that say that when Nadov and Avihu died, no aveilus followed their death. The Aveius was nidche because of the simcha of the Chanukas Hamishkan. But in a sense, the Medrash says, the "aveilus" came before they died, and this was an additional reason for the requirement that the Kohanim stay in the Ohel Moed for seven days prior to their inauguration. As it turns out, then, Nadav and Avihu sat Shiva for themselves.

In Moed Kattan 20a the Gemara learns the din of sitting shiva from a possuk in Amos 8:10, “vehafachti chageichem l’eivel,” I turn your holidays into mourning. Just as the shalosh regalim are seven days long, so, too, aveilus is seven days long. Tosfos asks why the gemara didn’t simply learn the law of shiva from a clearer– and earlier– reference, in Breishis 50:10, where Yosef was mis'abeil for Yaakov, where it says “vayaas le’aviv eivel shivas yamim.” Tosfos answers that we are looking for a case of real aveilus, which begins after the burial, and the ‘eivel’ in that passuk took place before Yaakov’s kvurah. He also brings the Yerushalmi that we don’t want to bring a rayah from before mattan Torah.

The Likutei Yehuda brings that one of the Gerer Rebbes (I don’t remember which one) saw an old sefer that said the following:

Even before the chet of the Eitz Hada’as, man would not have lived forever, because a world without death cannot exist. But before the chet, a man would decide when he had done all he was sent here to do, and all he was able to do, and he would get all his friends together, and make a celebratory seuda, and then he would go and die; he would simply stop living, just as the people of Luz would do. After the chet, people no longer know when they are going to die, and they don’t have a clear idea of what their purpose in life is, and they die whether they are ready or not. This change introduced the tragedy and fear and anxiety of death. Therefore, the ‘chag’ in the possuk in Amos the gemara brings– vehafachti chageichem– alludes to the valedictory celebration that would have accompanied death if not for the chet of Odom Horishon; that chag has been turned into eivel. This, then, is a reference to Adam in Gan Eiden, who long preceded the possuk of vayaas l’aviv eivel shiv’as yamim. So even without the Yerushalmi’s answer that we prefer to not bring psukim from before mattan Torah, the reason the Bavli chose the passuk in Amos was that the passuk of ‘ve’hafachti’, though written much later, refers to an event that long preceded the passuk of “vaya’as le’oviv eivel shiv’as yomim.”

These two ideas, that sometimes shiva can precede death, and that a levaya might be a celebration, are not mere theory. You have to wonder, how can the seven day isolation that accompanied the inauguration of the kohanim have been characterized as a pre-death shiva? What does that have to do with shiva? Perhaps the answer is that the seven days of isolation were a farewll to their past life, and now, as kohanim, they would have begun a completely new type of existence. That being the case, it was, in a sense, the same as the shiva that follows the death of a normal person. And as for the pre-Eitz Hada'as concept of death, I have attended levayos where, despite the attendant sadness, there was an undercurrent of the pre-expulsion feeling, where the person had had overcome so much and had acheived so much, that the levaya was as much a celebration of a life well lived as it was a tearful farewell.