Batman: Arkham City
After Batman was trapped in the Steel Mill under rubble, as a result of the attack of TYGER helicopters as part of Protocol 10, and being at the mercy of the Joker, Talia appeared out of nowhere and presented her ceremonial sword to the Joker, offering him to spare Batman's life in exchange for leading the League of Assassins and gaining immortality; Joker eagerly accepts the offer and takes the sword with him and they both leave.
After Batman is freed by Catwoman and forced first to stop Protocol 10, he makes it to Wonder Tower and shuts it down, resulting in the deaths of Ra's and Hugo Strange. Batman then goes to the Monarch Theatre where Joker is keeping Talia hostage and after defeating his snipers, enters the theatre where Joker requests the cure for the Titan Disease. Batman is confused as he thought Joker already had the cure; amidst the confusion, Talia easily overpowered the Joker and stabs him from behind with her sword, supposedly killing him.
She then reveals she got the cure from Harley Quinn. Batman manages to piece together that there have always been two Jokers but is too late as Talia is fatally shot in the back by the real sickly Joker, who reveals that the Joker double is in fact Clayface, who takes on his natural monstrous clay form and absorbs the cure in him, along with Talia's sword, sticking out of his shoulder. After a brutal battle, Batman manages to freeze up Clayface and after retrieving Talia's sword, uses it to slice Clayface into pieces. After making a tasteless joke about Talia's death, Joker detonates the rigged floor of the theatre, sending Batman and Clayface down the Chamber of the Demon in Wonder City where the Lazarus Pit is. Batman again uses Talia's sword to slice Clayface's clay minions, and after entering Clayface, uses the sword to permanently incapacitate him and retrieve the cure.
After Batman drinks half of the cure, Joker prepares to jump in the pit to achieve immortality, but Batman manages to stop him in time and also symbolically retaliate for Talia's death by throwing her sword into the pit's main generator controls, causing one of the generators to collapse and push Clayface into the pit, contaminating it because of his matter and creating a explosion that destroys the pit and most of the room. Joker attempts to steal the cure from Batman by force and as a result, Batman accidentally drops it on the ground, shattering it and rendering useless. After Batman tells Joker he would have saved him anyway, Joker gets the last laugh on Batman, laughing at the irony, before succumbing to the Titan Disease and dying.
After Batman: Arkham City
Following the closure of Arkham City, Batman had many of the incarcerated villains' personal equipment and items transported to the GCPD where after they were processed and analyzed, were kept in the GCPD Evidence Archive behind glass in a museum-like display, with Aaron Cash's voice serving as an introduction for the exhibits. Among the stored items was Talia's sword, which Batman had retrieved from the Chamber of the Demon sometime.
Batman: Arkham Knight
Talia's sword was kept behind glass in the GCPD Evidence Archive. When Batman visits the GCPD and interacts with Talia's display, he will touch the glass and quietly say her name before saying "I'm sorry", which shows that he still blames himself for Talia's death.