If I steal a character with Ward (from True Steel), and the character subsequently dies, can I react with, say, Arya Stark, or has the character lost the Stark affiliation by that point?

Alex

Interrupts precede their triggering condition.

Interrupts precede their triggering condition.

While true, Arya is not an interrupt, nor is any aspect of Ward .

The character left play, Ward was discarded - but it was a Stark character that was killed. Arya only cares that her triggering condition has been met, not whether the character actually ended up in the dead pile as a stark (or at all, if we get Benjen-like replacement effects).

Arya can react to a character you placed Ward on dying, provided it met the criteria (stark (from ward) character (yup) you control) at the time of death.

Sorry, I didn't feel like looking up spoilers for a card that's only been revealed in Sokovia, so I took a stab at it.

Generally speaking, triggering conditions do not change once they are created, even when the game state changes because of the expiration of continuous effects, earlier reactions, etc. The character had the Stark affiliation when it died, so an "after a Stark character is killed" triggering condition is created -- even though the character lost the Stark affiliation immediately upon being removed from the board.

This is effectively the same reason why using Put to the Sword to kill the only defender after you win does not change the challenge you won into an unopposed challenge -- it was opposed when you won it.