Redemption has long been a key theme in Star Wars, starting with Anakin Skywalker's return from the Dark Side in the Original Trilogy. Anakin's grandson, Ben Solo, similarly came back to the Light Side prior to his death in The Rise of Skywalker, and even the Clone Wars animated series' antagonist Asajj Ventress was able to renounce the Sith well before the end of her life. Jedi Master Yoda, on the other hand, was never able to bring his former Padawan Count Dooku back from the darkness, making their relationship one of the more tragic ones in all of Star Wars.
In many ways, Dooku's story began as sadly as it ended. As detailed in the 2019 audiobook Dooku: Lost Jedi, Dooku was born on the world Serenno to the planet's rulers, Count Gora and Countess Anya. Because his ancestors had retaken the world after defeating the members of the Sith Empire who once controlled it, Gora was terrified to learn his son was Force-sensitive. For that reason, he practically demanded the Jedi Order take Dooku away at a young age and cruelly left him for dead in Serenno's wilderness while he waited for their arrival.
Due to his regal manner and determination to excel beyond his peers, Dooku led a fairly lonely life as a Jedi youngling. His only real companionship was with his fellow youngling Sifo-Dyas and, on fewer occasions, Jedi Masters like Yoda. In time, Dooku also became fascinated by the Jedi Lene Kostana and her quest to recover relics connected to the Dark Side, which is why he aspired to become her Padawan. It wasn't to be, though; even after Dooku defeated Sifo-Dyas in a lightsaber tournament, Kostana selected the latter to be her new apprentice, much to Dooku's disappointment.
Of course, Dooku felt differently when Yoda decided to make him his Padawan instead. The pair subsequently went on a variety of training missions together across the galaxy, allowing Dooku to attain the rank of Jedi Master and secure a spot on the Jedi High Council. Yet Dooku grew disillusioned with the Jedi, believing they had become much too tolerant of political corruption within the Galactic Republic. This ultimately led to him leaving the Order and, sometime later, become the apprentice of the Sith Lord Darth Sidious, who recognized he could use Dooku's frustration with the Republic to serve his purposes.
At first, Yoda and the Jedi High Council were hesitant to denounce Dooku when he re-emerged as a leader of the Separatist movement, believing him to be a political idealist. That quickly changed, however, when Dooku aligned himself with power-hungry organizations like the Trade Federation and began amassing his droid army to take on the Republic. Flanked by the Republic's newfound clone army, Yoda and the Jedi sought out Dooku in what would become known as the First Battle of Geonosis, as seen in Attack of the Clones. It was there Yoda fought his former Padawan in a lightsaber duel and realized he had fully given himself to the Dark Side.
Despite everything, Yoda refused to give up on his old apprentice. In the short story "Sharing the Same Face," a canon novelization of the Clone Wars episode "Ambush" from the 2020 anthology book The Clone Wars: Stories of Light and Dark, it's revealed Yoda undertook a secret mission to meet the Toydarian King Katuunko in the hopes it would lead to an encounter with Dooku. What's more, Yoda believed there was a chance he could bring Dooku back to the Light Side, ending the war "without further misery and ruin."
Sadly, such a meeting never came to pass and the Clone Wars waged on for years. In fact, as depicted in the 2015 book Dark Disciple: A Clone Wars Novel, the Jedi eventually became desperate enough to send one of their own, Quinlan Vos, to try and assassinate Dooku to end the conflict. Still, knowing Yoda held on to hope that Dooku could be saved for as long as possible, it begs the question of what might've happened had fate brought the pair together early on during the war. In the end, though, it wasn't meant to be and the bond they once had was left forever shattered.