Count Dooku's Fall to the Dark Side and Yoda's Guilt
One of the most heartbreaking things explored in Star Wars: The Clone Wars is Count Dooku's fall to the dark side and how it impacted Yoda. While there isn't a lot of time devoted to it, there is enough to see that losing his apprentice broke him. Just as with his vision of a dying Ahsoka after she has already left the Jedi Order, it is clear that Yoda feels the weight of guilt and responsibility for the fall of his apprentice.
Yoda confronts Count Dooku on Geonosis in Star Wars: Attack of the Clones
In The Clone Wars season 6, episode 13, 'Sacrifice,' Yoda travels to the Sith planet of Moraband, to complete the trials to see if he is worthy of learning to become a Force ghost after death. Once he lands, both Palpatine and Dooku sense his presence. Palpatine immediately calls Dooku to Coruscant, and the two perform a ritual in which they use Dooku's blood to amplify their connection to Yoda. Palpatine uses this amplified connection to attack Yoda through the Force, just like Luke did in Star Wars: The Last Jedi. This ritual works because of Dooku's previous Master-Apprentice bond with Yoda.
Christopher Lee as Count Dooku in Star Wars Attack of the Clones
Dooku's Master-Apprentice Bond With Yoda
At the beginning of the episode, Palpatine tells Dooku that 'only the presence of someone significant to you would allow you to sense this ripple through time and space.' Dooku immediately replies, 'My old master, Yoda.' Dooku doesn't even need Palpatine to tell him who has gone to Moraband - he knows right away who it is. This shows that Dooku and Yoda still have a Master-Apprentice bond years after Dooku chose to leave the Jedi and become a Sith Apprentice. Not only that, but the bond is strong enough for Dooku to sense the presence of the Jedi Grand Master solar systems away. This shows a powerful connection between the two.
Count Dooku with a lightsaber in Attack of the Clones.
Not only is Yoda and Dooku's Master-Apprentice bond strong enough for Dooku to sense him light years away, but it is strong enough that Palpatine can use Dooku's blood to bolster a connection with Yoda. This suggests more than just a mediocre residual connection, but a deep attachment between the two. This is something that Palpatine exploits. While the ritual itself is a relatively short scene, it has great significance. Beyond showing the undying Master-Apprentice bond that still exists between Yoda and Dooku, the episode also demonstrates how conniving and cruel Palpatine is. He uses what Yoda cares about - and, for that matter, what Dooku cares about - to attack him.
Star Wars The Clone Wars Count Dooku and Savage Opress
The Vulnerability at the Heart of the Jedi
Choosing to train Dooku as his apprentice was an evilly brilliant move on Palpatine's part. Yoda is arguably the most powerful Jedi in existence. He is possibly the biggest threat to Palpatine's plans for galactic domination. This is likely why Palpatine chose to turn Yoda's apprentice to the dark side. Dooku's connection to Yoda can be exploited to allow Palpatine to attack him from afar, fighting the Jedi Grandmaster with no real risk to himself. As such, it creates a vulnerability at the heart of the Jedi. If Palpatine could eliminate Yoda, or even use Dooku to hurt him emotionally, the Jedi Order would lose its most powerful member.
Emperor Palpatine with his hands together and the Zillo Beast attacking Malastare from Star Wars: The Clone Wars
It is interesting to imagine what would happen if Yoda had met the Sith Lord again. It is clear from both Star Wars: The Clone Wars and the prequels that Palpatine was afraid of Yoda, which means he believed Yoda was a real threat. If Grandmaster Yoda had gotten another chance to meet Palpatine face-to-face, it is possible that he could have been the one to kill him rather than Darth Vader.
Count Dooku and Mace Windu appear in Tales of the Jedi.