While it's not typically labeled as "rotting fish soup," some traditional fermented fish products or dishes with a strong, aged fish component might have a very pungent smell that some people could describe as being similar to "rotting fish" if they are not accustomed to it.
For example:
Surströmming (Sweden): This is fermented Baltic Sea herring. It has an extremely strong, often described as pungent or even foul, odor and taste. While it's intentionally fermented, not "rotting" in the sense of being spoiled and unsafe, its aroma can be very off-putting to those unfamiliar with it. It's usually eaten as a delicacy, often with thin bread, potatoes, and onions.
Hákarl (Iceland): This is fermented shark. The process involves burying the shark meat to allow it to ferment, which neutralizes toxins and develops a very strong, ammoniac smell and a distinct, acquired taste. It's not a "soup," but it's a fermented fish product with a potent aroma.
Fish Sauce (Southeast Asia): While used as a condiment rather than a soup on its own, fish sauce (like Nuoc Mam in Vietnam or Nam Pla in Thailand) is made from anchovies or other small fish that are heavily salted and fermented for months or even years. High-quality fish sauce has a rich, savory (umami) flavor, but the fermentation process gives it a very strong, distinct, and sometimes intensely "fishy" or pungent aroma that some might find reminiscent of decay if they aren't used to it.
These products are carefully prepared through fermentation processes, which preserve them and create unique flavors, rather than simply being "rotting." The perception of their smell is highly subjective and culturally influenced.