The reign of the Mikaelson family is officially over. In The Originals Season 4 finale "The Feast of All Sinners," Klaus, Elijah, Rebekah, and Kol said goodbye to each other for good in order to save Hope from the Hollow, but Elijah took his exile one step further. What happened to Elijah on The Originals broke his blind loyalty to Klaus, but it also took away who he is. Allow me to explain.
In order to stop the Hollow on The Originals, Vincent needed four original vamps to volunteer to take one fourth of the Hollow's soul and power into their bodies. To keep the Hollow separated and unable to form again, Klaus, Elijah, Rebekah, and Kol can never see each other again. Moreover, they can never see Hope. If they do, the Hollow inside of them will want to be reunited, which could result in the Hollow's resurrection. Other than the fact that this means the end of Haylijah and the end of Klaus' relationship with Hope, it also puts Elijah in an impossible position. As Rebekah points out, there is no way Klaus will be able to survive without his family. Eventually, Klaus will lose it, and Elijah will feel compelled to swoop in and save him from himself just like he always does. Before they perform the ritual to save Hope, Klaus makes Elijah promise that he will let Klaus go, but Elijah, the gentleman that he is, can't do it — not without help. After the ritual, Elijah asks Vincent and Marcel to do him one last favor: have Marcel compel him to forget his allegiance to Klaus.
But Marcel doesn't just compel Elijah not to rescue Klaus. In order to truly ensure that he never sees his brother again, Marcel essentially erases Elijah's memories. No more love, pain, loyalty, or Mikaelson drama — as far as Elijah is concerned, it's all gone. In fact, when Klaus visits him in a village in France some time later, Elijah doesn't even seem to recognize his brother at all.
For now, it looks like erasing Elijah's memories has left him at peace, but that could easily change. Who is Elijah without the love of his family or the memory of his love for Hayley? What if Elijah turns back into the monster Hayely saw in the pendant? I guess we'll find out in Season 5!