I attempted to find anything George RR Martin might have said about the character but other than what we've been told in the books and TV show we have not been made aware of Syrio's fate. I'm largely going to go off the books standpoint as it has more description regarding the final scene he appears. We know Syrio is fighting six men, five Lannister soldiers and Ser Meryn Trant of the Kingsguard. Syrio continuously refers to himself as the former first sword of Braavos indicating he is well trained and the mere fact he chooses to hold off the soldiers with a wooden practice sword while Arya of who he must be aware is of utmost importance to Cersei if she is sending that many to capture her. Syrio proceeds to best the five Lannister soldiers possibly killing one of them in the process (could be two, been a while since I read the first book).
He then fights Ser Meryn Trant who he lands several ineffective blows on due to the kingsguards heavy armour who proceeds to brake his practice sword. Usually the kingsguard are considered to be the most elite fighters in the Seven Kingdoms although Syrio continues fighting Trant despite his broken sword it is not too far fetched to think Syrio escaped. Eddard Stark himself tells Bran that he no longer believes the kingsguard to be the finest soldiers especially as he fought against Ser Arthur Dayne (The Sword of the Morning), Ser Gerald Hightower and Ser Oswell Whent who were considered the last amongst the greatest of the Kingsguard. Ser Jaime Lannister (the Kingslayer) is perhaps the only member of the current order who meets the required standards and he confesses he believes Ser Arthur Dayne himself would be ashamed of what their order has become.
Jaime goes on further to berate Ser Meryn for his actions informing him that their first duty is to protect the monarch even if it means protecting them from themself and to use his common sense when given questionable orders such as beating women and children in relation to Meryn's actions towards Sansa Stark. Meryn is not considered to be that good a knight and the majority of the Kingsguard with the exception of Ser Barristen Selmy and Ser Jaime Lannister are considered to be filling vacant positions. Syrio himself berates Meryn calling him slow for a Kingsguard after Meryn tries to slander him by saying Syrio is quick for a dancing master. With only Meryn blocking Syrio who proves himself to be a more than capable fighter in only a few lines with a wooden sword than Ser Meryn seems to have managed so far in the entire series I am highly skeptical that he alone could stop Syrio from getting away and is more than likely to have been either knocked down or slipped past due to his armour weighing him down and his slowness Syrio probably could have managed it without injuring Meryn much if at all.
Furthermore the relation between Syrio Forrel and Jaqen H'Ghar that many people have theorised may not be that far wrong. If they are the same person providing Syrio escaped what is to say he did not decide the best way to escape was by disguising himself as a prisoner being taken to the wall as a faceless man it would not be that difficult to take such a prisoners place the only question surrounding that would be why choose to be a prisoner who is locked in a wagon but maybe he wasn't originally perhaps Yoren put him there after seeing him fight off some Lannisters whilst preparing to leave or maybe Yoren got in the way and Jaqen fought with him to get put in the cage where the Lannisters would simply overlook him. Jaqen also seems to not care for murdering Lannisters when he masquerades as one and is curiously interested in Arya even before she helps him to escape being burnt alive and is more than willing to help her repay the Red God with three deaths especially when he helps kill several guards so she and her party can escape therefore over paying the Red God. Along with this Syrio believes there is only one God, death.
Jaqen seems to believe in the Lord of Light (one God, despite what Melisandre says to Gendry) and even then it is all to do with death essentially stealing three lives from death she has to give death back three lives. The Faceless Men themselves don't seem to care what they do whilst working up to an assassination and they do say it can take years perhaps if Syrio is such then he may have taken the job to train Arya to get close to a possible target in Westeros which could have been King Robert himself as he has many people who call him usurper still and so he can leave King's Landing or maybe such role was simply a means to an end if he indeed is serving the Lord of Light as well then perhaps they had seen a vision of Arya and he was sent to watch over her particular as she ends up in Braavos but I will say no more on that. That's my theory anyway as to how Syrio could have escaped and his possible relation to Jaqen H'Ghar.