Like in the show, in the books Ser Meryn breaks Syrio's wooden sword, and Arya flees the scene before they resume fighting, so we don't know for sure what happens.
Syrio isn't seen again, and Ser Meryn makes no reference to the incident throughout the rest of the series.
The general consensus seems that he is dead, seeing as, like the Hound so eloquently puts it, "Your friend's dead and Meryn Trant's not 'cause Trant had armor and a big fucking sword.".
But of course, it is possible that he escaped, as he displayed a supremely good prowess in combat, even when unarmed, versus the Lannister soldiers.
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It has not been confirmed one way or the other in the books or show.
However, Race for the Iron Throne has an excellent post arguing Syrio's survival would be totally against the underlying themes of the story: Syrio Forel is dead, and has to be dead, and would probably be offended if someone tried to bring him back to life.
In a dramatic sense, Syrio has to die because he’s The Mentor – and the Mentor always dies in the hero’s journey to raise the stakes (since the hero is now alone and unprotected) but also to allow the hero to begin their process of maturity and becoming independent (since the hero now has to stand on their own two feet without hints).
It goes on to say: [What] matters is that Syrio stands up for the right and defies evil, even when that means facing a knight of the Kingsguard with a broken practice sword, not that Syrio succeeds.
The whole piece is well worth reading.
This is circumstantial, and as far as I know George RR Martin has neither confirmed nor denied it, but it makes a strong case that Syrio Forel is in fact dead.
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One thing that I always thought suggested he was still alive was his total confidence.
He showed little regard for the Lannister guards he beat with his wooden sword, but after beating them and squaring up to fight a Kingsguard, he doesn't even bother picking up a steel sword of any of the guards he just knocked out.
I get the impression death came calling for him
and he said "Not today"
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In 2005, GRRM pointed out that Syrio seems to have been left in a hopeless situation when he was last seen, and suggested readers should "draw your own conclusions" based on this, which seems to imply that Syrio Forel was in fact killed.
More recent reports (but, it should be said, unconfirmed) indicate GRRM does not understand why he gets asked the question repeatedly, pointing out that Syrio is not immortal; if accurate, this seems to more heavily imply that Syrio Forel is dead.
Source: http://www.westeros.org/Citadel/FAQ/Entry/Is_Syrio_dead
It's quite possible that he is neither alive nor dead, i.e. perhaps GRRM never concluded in his notes or otherwise the true fate of Syrio.
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We don't really have any evidence, but I believe that he has died.
The Lannisters killed all Stark partisans out of hand; they even killed Septa Mordane, who was completely harmless.
Syrio was a friend of the Starks and he even fought back, so it is not really hard to imagine that the guards killed him.
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In the scene where Arya runs away and looks back you can hear metal swords falling down which hints that syrio could have made it out.
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We finally have conformation.
Syrio Forel is dead and is not Jaqen H'ghar
I was really diapointed to hear this, but we finally have confirmation that he is neither Jaqen H'ghar or still alive.
Showrunners David Benioff and D.B. Weiss have confirmed this.
"I always was like, 'Oh, no, I feel like he's still alive,'" Williams told IGN.
"I always had my own theory that he and Jaqen [the Faceless Man] were the same person."
But when she finally ran the idea by showrunners David Benioff and D.B. Weiss, they shot it down without hesitation:
Forel is dead.
"I was like, 'Oh, OK," Williams said, laughing. "
So that put that to bed really quickly, but I guess we can all still dream." Syrio Forel alive or dead?
Game of Thrones showrunners finally give definitive answer
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I wondered the same myself when I read the scene of his alleged killing (I started reading after watching the show).
In the show it is clearly hinted that he's dead because we can hear his (probably) scream when Arya is running away.
But in the books there's no scream, his death is not shown in any way; in addition to that in the books he's shown to have killed and/or severely injured 5 of Lannister guards before he was attacked by Ser Meryn, in other words he's described to be much more dangerous and fast than in the show.
So, after watching the show I actually didn't even stop to think that Syrio may be alive, but the book made me wonder.
Of course it's unlikely that he could've survived a fight against a fully-armored knight.
On the other hand, judging from the movements and fighting stance, Bronn seems totally like a Water Dancer to me (he's decribed to be very fast and he uses a one-handed sword and doesn't use a shield, exactly like Syrio) and he defeated a fully-armored knight (of course, armored with a real sword; his style is also more passive and treacherous than that of Syrio's).
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I think Syrio may be alive.
Ser Meryn Trant was in the King's Guard, while the defeated guards were Lannister guards.
Trant's skills may have surpassed that Lannister guards, but once Arya fled, he'd understand the value of interrogating Syrio rather than killing him.
After Arya's successful escape, Syrio would have little reason to continue fighting, unless his life was truly in danger.
With swords laying around from the bested guards, it seems likely that Syrio could grab one.
At the least, he could have escaped and outrun a larger man in heavy armor.
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In the episode 'The Pointy End' (Season 1 Episode 8) when Arya runs from the Lannister guards you hear the sound of a sword being dropped (around 4:56):     After that neither Syrio or Ser Meryn Trant is never mentioned or seen in the show again, except when Arya mentions to the Hound that Ser Meryn Trant killed Syrio.  Is there any mention in the books that Syrio actually dies?
Is Syrio Forel dead?
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The general consensus seems that he is dead. It has not been confirmed one way or the other in the books or show.   Syria Forel is dead and is killed by Ser Merton Trant and the Lannister soldiers sent by Cersei to capture Arya though there is a minute chance he might be alive if he managed to grab a sword from the bested guards.
Syria Forel is dead. Syria Forel is killed by Ser Merton Trant and the Lannister soldiers sent by Cersei to capture Arya. Syria Forel, though unlikely, perhaps managed to grab a sword from the bested guards and is still alive today.