For the source text click/tap here: Pesachim 78
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The Mishnah teaches that the Korban Pesach may be offered only if its meat may be eaten. If the meat became Tamei, then the Korban may not be offered, because the purpose of offering the Korban Pesach is to eat it.
When any other type of Korban becomes Tamei, the Korban may be offered as long as even one k'Zayis of meat or fat is still Tahor.
Furthermore in a situation where the majority of the public is ritually impure, in which case everyone agrees that they perform the ritual of the Paschal lamb even in a state of impurity.
These unique halachot regarding impurity lead us to understanding when and why the seder continued without the Korban Pesach after the Hurban
And why there a those in the 19th century who felt we could begin again bringing this unique Korban.