During the Battle of Winterfell, Alys and a group of Karstark archers join Theon and the ironborn in defending Bran. She is killed when the wights overrun the godswood. Her death renders House Karstark extinct.

Why was Karstark beheaded?

He openly insults the King in the North and claims the war is a lost cause. Remaining true to his honor just like his father, Robb decides that Lord Karstark must die for his treason. ... Rickard is executed for treason by Robb.

Is House Karstark extinct?

House Karstark became extinct when Alys was killed during the Battle of Winterfell.