You can try Archive of Our Own (AO3). It has a large collection of fanfictions, and you can search for 'Merlin exhausted' specifically in the search bar. There are likely to be many stories there.
Some Merlin - focused fan communities or forums might have members sharing their own 'Merlin exhausted' fanfictions or know where to find them. For example, certain Tumblr groups dedicated to Merlin might have posts or links to such stories. You can join these communities and start exploring.
Fanfiction.net is also a good place to look. Look for the Merlin section and then use the search function to find stories related to Merlin being exhausted. However, the quality may vary, so you might need to sift through a few to find the really good ones.
One good 'Merlin exhausted' fanfiction could be 'Merlin's Tiring Day' where Merlin has to deal with multiple magical threats in one day and is completely worn out by the end. It shows his struggle and how he overcomes it despite his exhaustion.
It could also be due to the lack of proper rest. Merlin is usually depicted as a very busy character in fanfiction. He has duties in the castle, like serving Arthur, and on top of that, he has to use his magic to help those in need secretly. With so much to do, he might not have enough time to rest, leading to exhaustion.
In a more humorous take on the 'Merlin tied to a bed' fanfiction, it could be that Merlin has fallen ill and the overly - protective Gaius has tied him to the bed to make sure he rests. Merlin, being the active person he is, complains constantly. Arthur comes to visit and teases Merlin about finally being still for once. Meanwhile, Merlin tries to convince Arthur to let him loose, promising that he'll be fine. Eventually, Gaius relents and unties Merlin, who then immediately starts bustling around the room.
It could be for comedic effect to lighten the mood and add some fun to the story.
If Merlin died in the fanfiction, it could trigger a series of tragic events. The balance of power could tip, and the villains might seize the opportunity to attack. It could also bring out hidden strengths in the remaining characters as they try to cope with the loss.
If Merlin is a Dark Lord in fanfiction, it could be an interesting exploration of the 'nature vs. nurture' concept. Maybe he turned dark because of the constant fear of being discovered and persecuted for his magic. His actions as a Dark Lord might include taking over Camelot or exacting revenge on those who wronged him in the past. It gives a whole new perspective on his character.
One more idea is that Merlin is tied to the bed in a dream - like state created by an ancient magic. In this dream world, he is faced with his deepest fears and insecurities. His friends in the real world notice his strange behavior and try to wake him up. Merlin, while in the dream, has to find the source of the magic that is binding him and break free. Through his inner strength and the memories of his friends, he manages to do so and wakes up, having learned more about himself and his magic.
The 'exhausted Tony Stark' theme is popular because it makes him more relatable. Everyone gets tired, even a genius billionaire playboy philanthropist. It adds depth to his character.
He could become a Dark Lord due to betrayal. If someone he trusted deeply, like Arthur perhaps, turned on him because of his magic, it might push him over the edge.
One possible reason could be a magical curse. In many Merlin fanfictions, magic is often used as a plot device. A dark sorcerer might cast a spell on Merlin to make him forget certain things, perhaps to prevent him from using his powerful magic to oppose them. Another reason could be a self - imposed forgetting due to trauma. Merlin has witnessed and endured a great deal of pain and suffering. To protect his own mental state, his mind might subconsciously block out certain memories.