Typically, an anime would end with the heroes defeating the antagonists either peacefully or by force. That being said, there are some uncommon instances where the hero doesn't just lose but actively allowed their opponent to win.
Sometimes, this was because the protagonist lost the will to fight, or they were just powerless in the face of forces beyond their control. This didn't make these main characters bad by any stretch, though it did give them more depth than expected.
WARNING: Spoilers ahead.
10 SK8 The Infinity — Reki Kyan Enjoyed His Second Loss To Adam
Midway through his time on the S, Reki realized how far away he was from his genius friends in terms of raw talent. Not helping was his devastating loss to Adam, which really did a number on his ego. While brooding and moping to himself for a few days, Reki remembered the reason why he got into skating in the first place: it was fun.
After apologizing to his friends and especially to Langa, Reki faced Adam once again on the asphalt. This time, though, Reki didn't let Adam intimidate him and even made a fool of the Matador of Love. Reki lost to Adam, but this wasn't a bad thing, since winning wasn't as big a priority as rediscovering his love and passion for skating.
9 Tower Of God — Everyone Unknowingly Pledged To Help Rachel Win
After Rachel suffered a paralyzing injury and failed the latest test, she was summarily eliminated from the Tower's competition for godhood. Bam, who would give his life for Rachel, volunteered to take the deadly Administrator's Test. If he succeeded, Rachel would proceed to the next round. If he failed, he would die.
Just when Bam was close to beating the test, a healthy Rachel stood from her wheelchair and pushed Bam into the abyss. Rachel (who was lying this whole time) then manipulated the remaining participants into helping her get to the Tower's top to honor Bam's "death." Khun was the only one to suspect something, but he hadn't yet put the pieces together.
8 Black Lagoon — Rock Orchestrated Roberta's Successful Revenge
During Roberta's Blood Trail, Roberta returned to Roanapur with a vengeance. Roberta's target was the American black ops unit Grey Fox, but she didn't care about killing whoever else got in her way. To stop her from burning Roanapur to the ground, Rock offered an unorthodox solution: give Roberta exactly what she wanted.
By striking deals with the criminal echelon and emotionally manipulating everyone including Roberta's young master Garcia Lovelace, Rock drew Roberta out into the Golden Triangle, where she ruthlessly hunted down Grey Fox to her heart's content. The price, however, was that everybody (including Revy) now distrusted and feared Rock.
7 Attack On Titan — Erwin Smith Let The Beast Titan Wipe Out The Survey Corps' Remnants
The mission to reclaim Shiganshina and, by extension, Wall Maria was so dire that by the end, almost all of the Survey Corps was killed. That said, the highest casualty rate was deliberate on Erwin's part. Specifically, Erwin led the corps in a suicide charge against the Beast Titan, who was dominating the battlefield with his handheld projectile bombardments.
Zeke Yaeger may have killed the soldiers who were giving him a hard time, but this was a step towards his defeat. Erwin's charge was the bait in Levi Ackerman's strategy, since he needed a distraction to get close to the Beast Titan. Even though Zeke barely escaped with his life, the Corps' sacrifice didn't go to waste as they successfully reclaimed Wall Maria.
6 Death Note — The Japanese Task Force Unknowingly Helped Kira Evade Justice
When Kira (Light Yagami's god persona) first came to power, the world's authorities found themselves out of their depths. In desperation, Interpol reached out to the master detective L, who gave the law enforcement agencies tracking down Kira an edge. But then halfway through the anime, Kira bested L and killed him and his loyal butler, Watari.
Though demoralized and terrified, the investigators pushed on with Light as their new leader. Because they had yet to realize that their new boss was actually the self-proclaimed God of the New World, the Japanese Task Force inadvertently helped Light cover his tracks and exact his unforgiving brand of justice from the shadows for the next five years.
5 Blue Gender — Yuji Kaido Let Gaia Wipe Out Humanity
The twist of the nihilistic Blue Gender was that the monstrous bugs called the Blue weren't aliens, but creatures born from Earth. In brief, Gaia (aka the planet's sentient spirit) created the Blue to kill humanity in the name of purifying the Earth. When Yuji discovered the planet's absolutist will, he basically decided to let Gaia carry on with what it was doing.
To be fair, Yuji didn't explicitly tell Gaia to kill, since he discovered that the Earth was finally rejuvenated and ready to give mankind a second chance. After this understanding, it's implied that Gaia drove the people of the orbital Second Earth mad, leading them to kill each other. For whatever reason, Yuji had no problem with Gaia killing off the other survivors.
4 Wonder Egg Priority — The Girls Moved On From Frill & The Egg World
Besides its unsatisfyingly abrupt conclusion, Wonder Egg Priority also became infamous after its heroes just gave up. To be fair, this was understandable. Besides Momoe and Rika seeing their loyal Pomanders get brutally murdered, they and Ai discovered that their revived friends were parallel world variants and that Neiru was an artificial human.
After the trauma, lies, and empty promises that Acca and Ura-Acca put them through, the girls just stopped going to the Egg World and abandoned the mystery of Frill's connection to girls' suicides. The truth of Neiru was the last straw for Momoe and Rika, who moved on with their lives while Ai only decided to go back for Neiru months later.
3 Psycho-Pass — Akane Tsunemori Begrudgingly Forged A Truce With The Sibyl System
For her whole life, Akane was under the impression that the Sibyl System was just a really smart and effective AI algorithm. In truth, Sibyl was a hive mind of the disembodied brains of the worst known sociopaths, who now collectively controlled every facet of Japanese society. Knowing that Akane valued justice, Sibyl used this to their advantage to strike a truce.
Near Psycho-Pass' end, Sibyl asks Akane to help them capture or execute Shogo Makishima. Akane begrudgingly complied since she understood Sibyl's necessity in maintaining order, though she vehemently disagreed with their methods. The anime ended with Akane not exposing Sibyl's truth or usurping its rule but promising that someone in the future would.
2 Puella Magi Madoka Magica — The Magical Girls Couldn't Stop Homura Akemi's New World
The third Madoka movie, Rebellion, shocked everyone when it ended with Homura usurping Madoka's godhood to become evil incarnate. With her newfound powers, Homura rewrote the world into a false paradise that resembled a peaceful school-life anime. While all the magical girls had their memories wiped, Sayaka still had hers and confronted Homura.
Despite Sayaka's determination and moral high ground, she was still outmatched by Homura. In the end, Sayaka's memories reset, and she too fell victim to the new world. Homura's victory, however, is only fleeting since Madoka Kaname will inevitably regain her memories - which was all but confirmed by the announcement of the sequel, Walpurgisnacht Rising.
1 Re:Creators — The Creators & Creations Reunited Altair With Her Beloved Creator
When Altair literally broke the fourth wall to enter the physical plane, her goal was the avenge Setsuna Shimazaki. Previously, Setsuna took her own life after she felt as if the world (especially her friend Sota) abandoned her. Her favorite original character, the Military Uniform Princess, then came to life to end both the real and fictional worlds in her name.
After futilely fighting her, the Creators and Creations realized that the best course of action was to give Altair what she wanted. Using Sota's memories, the Creators perfectly recreated Setsuna and reunited her with a shocked Altair. After some hesitation, Altair embraced the new Setsuna and abandoned revenge for a new reality just for the two of them.