Hi.
Jaqen H'gar is:
Any Phase: Bring Jaqen H'ghar out of Shadows by paying the rest of his cost to choose 1 non-Army character in an opponent's dead pile that was killed this phase, and attach it to Jaqen H'ghar as a duplicate. Jaqen H'ghar gains the printed text, base STR, icons, traits and crests of that card. If that duplicate leaves play, return Jaqen H'ghar to Shadows.
What happens if he's in play and then burned, i.e. its strength reaches 0 and is killed/discarded if its strength is 0?
Thank you