[Theory] How Madara did -not- die. Chapter 626 spoilers ahead.
As we all know, Madara was somehow still alive when he met Obito. He had the Rinnegan and Senju DNA inside him.
Since Edo Tensei is not perfect and I cannot picture Tobirama using a perfect version of it to raise Madara, I am going to assume that was the master move in Madara's plan to acquire Hashirama's DNA. It is clear to me that he read the requirements for Rinnegan on the tablet - Senju and Uchiha DNA.
So, I propose this.
Madara knew he was losing the moment he lost the Kyuubi. So, what does he do? He realises he can't win and uses Tsukuyomi on Hashirama.
Note the moon ( Eye of the Moon Plan, the Moon has started to be a symbol for Tsukuyomi and if I am not mistaken in Japanese mythology Tsukuyomi is linked to the Moon ) and the close shot on his EMS.
I do not believe Madara would have fallen for his Mokubunshin. Not when he said this.
Why would he lie to the Gokage? Make himself seem stronger? He was already stomping them. No. I believe Madara saw through the bunshin and let Hashirama stab him, using Tsukuyomi to make him think he fatally wounded him, when in reality he probably missed his heart.
With Hashirama 100% dedicated to the Village and thinking Madara was dead, Madara now had a clear path to obtain the Rinnegan and plan his revenge.
He had Hashi's DNA and the whole world thought he was dead, giving him a perfect cover and the only thing he needed for the Rinnegan.
Regarding Madara's wound. Look at this pic.
and then this
In the first one, Madara is stabbed straight through the middle of his chest, i.e. his heart. This is from Hashirama's POV who, based on my theory, is under genjutsu and thinks he killed Madara.
In the second we clearly see the wound is slightly to the left, which suggests Hashirama missed his heart.