Can I get a refresher here? Are you talking about Jaquen? Was it known he was there until Arya was on her way north?
Well, we know Jaqen was in the Black Cells at the same time as Ned since Yoren said that is where he got Jaqen, Rorge, and Biter from.
Here is where the theory starts:
Faceless men are the world's premiere assassins. From what we have seen of Arya's training and Jaqen's abilities it seems highly unlikely that he was just caught and tossed in the dungeon. It seems far more likely that he was put there for a reason.
Going off of that premise - who would be Jaqen's potential target? The only person in the dungeons would be Ned. Also, the plan for Ned once he confessed to being a traitor was to go to The Wall with Yoren - so Jaqen is perfectly placed there as well. So - who wants Ned dead and who has had contact with Faceless men? Littlefinger.
Littlefinger hates the Starks - has for a long time. We also know that Littlefinger has approached/had dealings with the Faceless men (he talks about their prices when the Small Council is discussing killing Dany). We also know that Littlefinger's family was initially from Braavos (where the Faceless men reside). On top of that we know that Littlefinger wants chaos. Assuming that Littlefinger wants Ned dead it seems likely that he is the one that influenced Joffrey to execute him (and might have told Slynt since we know Slynt didn't hesitate when Joff called for Ned's head). However, if Cersei, or Varys, or anyone prevented the execution from happening - he has the backup plan of Jaqen going to The Wall. Jaqen is also very skilled about making deaths look like accidents. I wouldn't be surprised if Ned's death was to look like an accident or to look like a Lannister killed him.
This would also explain Jaqen knowing who Arya was when he came across her in the Harrenhal godswood.
I dont recall this exchange? Can you link it please?
I don't have a link or page number - but it is the scene where Arya is pissed off at the Heart tree/Old gods for not saving her father - so that would be one of the Arya chapters in A Clash of Kings. Jaqen says something like "The Old Gods shoudn't be mocked". During this conversation (IIRC) Arya asks Jaqen who he is and he says he has many names like she does "Arry, Weasel..... Arya" or something like that.
Arya IX
Arya went to her knees. She wasn't sure how she should begin. She clasped her hands together. Help me, you old gods, she prayed silently. Help me get those men out of the dungeon so we can kill Ser Amory, and bring me home to Winterfell. Make me a water dancer and a wolf and not afraid again, ever.
Was that enough? Maybe she should pray aloud if she wanted the old gods to hear. Maybe she should pray longer. Sometimes her father had prayed a long time, she remembered. But the old gods had never helped him. Remembering that made her angry. "You should have saved him," she scolded the tree. "He prayed to you all the time. I don't care if you help me or not. I don't think you could even if you wanted to."
"Gods are not mocked, girl."
The voice startled her. She leapt to her feet and drew her wooden sword. Jaqen H'ghar stood so still in the darkness that he seemed one of the trees. "A man comes to hear a name. One and two and then comes three. A man would have done."
Arya lowered the splintery point toward the ground. "How did you know I was here?"
"A man sees. A man hears. A man knows."
She regarded him suspiciously. Had the gods sent him? "How'd you make the dog kill Weese? Did you call Rorge and Biter up from hell? Is Jaqen H'ghar your true name?"
"Some men have many names. Weasel. Arry. Arya."
She backed away from him, until she was pressed against the heart tree. "Did Gendry tell?"
"A man knows," he said again. "My lady of Stark."