Bloodlines can die when the last witch (non-active/active) dies ,without offspring and the bloodline can’t be continued. Any offspring is good to continue the bloodline. The death of a bloodline happens very rarely (only 2 have died within the existence of witches) because every single descendent of every branch (even non-active) has to die.
The bloodlines of the fourth and seventh witch have died. The bloodline of the fourth Witch was activated, but died. The bloodline of the seventh witch died , but was not active.
The fourth witch , Nerilla , had the special ability to control the element of water. Unfortunatly this meant that she was the opposite of Doraeha. When May Miller noticed this ,she felt that the tribe loyal to her (the Hainasoni) was in danger , and she sent her army to kill every single one of Nerilla’s descendants.
-add in activation-
The seventh witch , Ayla ,was the youngest but often to most underestimated. Her descendants are characterized by ferocity and fearfulness. It is also believed that descendants of the seventh witch practice dark magic that tap into the powers of death and cruelty. Therefore , the seventh bloodline was killed by followers of the Council of Elders because it was evolving into a dark bloodline. The name of this family was Garfunkle.