Because they have a death wish. One of them was a Warlock who had no magic of his own so he kidnapped Elijah to drain his magic. Broke his arm when he tried to escape.
Another time, our sister who was in the body of a witch--the witch gained control of the body again--she was evil and kidnapped many children and drained their power to make them stronger. We freed them and Rebekah from her clutches.
Lastly Elijah was kidnaped because I tried to save the girl from the clutches of a vampire who was unhinged, and we had to do a trade off.
He's been through hell and he blames himself for the life we had.