Well, the general consensus that I've heard is that it's an old recruit that Ezio personally trained that turned into a Templar. Not unlike Haytham Kenway. He also mentioned how much he liked Rome compared to Florence and Roma at the beginning of the games was considered Templar headquarters and Florence being controlled by the Assassins. Also there is a photo of the clothing of the man and it had the Templar cross.
The cannoncanon reason of death of Ezio is heartattackheart attack. So in my personal headcannonheadcanon the Templar saw that his old mentor was dying and even though they are opposite sides decided to somewhat comfort his old mentor at his time of passing and give him his respects.
Now my personal theory that I've had for a long time is that the man is death himself. Because just before the actual moment of death for Ezio the man grabs his arm and lightly touches his shoulder when he stood. Throughout different media in the real world where death is portrayed the way he does the final deed is they put their hand on them just as the man put his hand on Ezio. Which would explain why the man seemed to completely disappear.
Either way Ezio Auditore is best Assassin and I will fight you on it.