Zevachim 104 - Hides of Invalidated Offerings
If an offering became invalidated prior to being skinned, its hide does not go to the kohanim. Only if the offering was skinned before it became invalidated, then the kohanim get the hide. Rabbi Chanina, the long-time administrator of the kohanim says, "In all the days of my life I never saw an invalidated hide being burned" - meaning that the invalidation discussed above never happened. But the Sages say that "I never saw" is not a proof.
There are special sin-offerings, such as the goat brought for communal idol worship, that are not eaten but are burned in a designated place outside Jerusalem, called the place of ashes. These offerings contaminate the people who are carrying them, and they contaminate even the people's clothing. The offerings were carried out on poles. The first group of carriers becomes impure when it leaves the Courtyard, while the second group remains pure until they in their turn leave the Courtard. Rabbi Shimon says that none of them become impure until the fire catches onto the larger part of the sacrifice.
Art: Giovacchino Toma - The Rain Of Ashes, 1880