In The Originals series finale, brothers Elijah and Klaus Mikaelson died, staking each other with White Oak, and the show's spinoff Legacies addressed what happened next. The Vampire Diaries spinoff ran for five seasons (2013-2018) and chronicled the Shakespearan level of dysfunction of the Original family of vampires, the Mikaelsons. When they weren't battling each other, the Mikaelson clan faced a seemingly endless number of outside threats, including assorted foes they collected throughout their 1,000-year lifetimes. Eventually, it was the evil spirit of the Hollow that threatened to consume Klaus from the inside that led to his demise.
The Originals season 4 introduced the show's most formidable villain, the Hollow. In 500 A.D., two rival tribes arranged a marriage in an attempt to combine their power, hoping to unite their covens. The child born out of this union, Inadu, was "ruthless, unfeeling, and empty." The tribes killed her, but her spirit continued to possess various hosts, including Hope Mikaelson. Vincent Griffith performed a spell that divided the Hollow into the four Mikaelson siblings, and they scattered to prevent the Hollow from regaining her power. During season 5, the Hollow continued to have a stronghold on the Mikaelsons. Fifteen-year-old Hope cast a spell that transferred the Hollow from her family into her, and the darkness became so overpowering it endangered her life, so Klaus had the Saltzman twins siphon the Hollow from Hope and place it in his body. To eradicate the Hollow for good, Klaus decided to sacrifice himself. Elijah, who finally achieved his lifelong goal of witnessing Klaus' redemption, remained loyal to him until the end. Each brother drove a White Oak stake into the heart of the other.
Two years later, Hope still questioned her father's fate. In Legacies season 1, episode 7, "Death Keeps Knocking On My Door," the presence of the Necromancer only served to amplify her anxieties regarding Klaus. The Necromancer confronted Hope about her fears regarding her father. "You want to know if he's at peace or if he's suffering. Regretting his sacrifice. After all, he did die to save your life." This is the question that plagued fans as well who weren't thrilled about the anti-hero's death in The Originals season 5 finale. Eventually, the Necromancer told Hope that Klaus watches over her every day, he died with love in his heart, and he doesn't regret his choice. Sadly, Klaus won't find peace until Hope does.
Klaus wasn't sucked into a black void of nothingness but peace eludes him. There's also no mention of Elijah, who possibly reunited with Hayley Marshall. There is no Other Side, but Klaus lingers in a sort of purgatory. Does Klaus deserve peace? He may have become a devoted father, but he still committed innumerable despicable acts - many against members of his own family. He wasn't exactly someone who deserved a happy afterlife, but fans wouldn't have it any other way.
The Necromancer's revelation provided Hope with some closure. She decided to write Klaus a letter in honor of Remembrance Day. She promised to try and find peace within herself, and she looked forward to the day when he was no longer with her. Alaric warned Hope the Necromancer would use her parents to manipulate her. Of course, how much of what the Necromancer said was real could be revealed in future episodes, but the answers won't come from Klaus.