Edo Tensei uses a living corpse for the soul of the dead to inhabit. Rinne Tensei allows the dead to live again. (but are souls and spirits the same thing?) idk but w.e. This is the first time Edo Tensei summon was hit by a Rinne Tensei. Its weird and hasn't been explained . The soul inhabits the edo tensei body so that means the sacrifice becomes the body of the soul. So the soul has now the body of the sacrificed corpse.
ot: I wondered if when Obito used Rinne Tensei on Edo Madara, Madara's soul would return to his body in the cave. Based on something Kabuto said, Obito thought Orochimaru had already been gathering info about Zetsu(or hashi's senju dna). Hashirama's cells are living (even after he dies I think, how else could Danzo use them?)
Kabuto already knew about Zetsu when he met Obito , so He & Oro probably already got Madara's corpse from his underground cave, and used Zetsu/Hashirama's dna/cells to give Madara's corpse "life" or "living cells" and "fused" them into each other, so in a way his body was living just without a conscience.(conscious ?)
So Madara's corpse was used as his sacrifice for his soul to re-inhabit for the Edo Tensei summoning.
but wasn't really explained..(maybe kishi didn't think of an explanation.)