Pesachim 76 - Passover lamb must be eaten

We saw earlier that if the community of those who came to Jerusalem celebrate Passover is ritually impure, they can all offer the sacrifice nevertheless. The instruction to bring it in its appointed time includes even the time when the community is impure. Since the whole purpose of bringing the offering is to eat it, the appointed time applies to eating as well.

This is not always the case. There are five cases when the offering is brought but not eaten - when the community is impure. These other offerings may be flour or animal meat, and they would have to be burned. 

Art: Jerusalem from the Mount of Olives by Frederic Edwin Church