It Can Survive, but Its Survival Ability Is Limited
A goldfish can still survive without a tail, but its survival ability and quality of life will be significantly affected. Here is a detailed analysis:

The Possibility of Survival
Even if a goldfish loses its tail, it can still survive. For example, a goldfish had its tail rot away due to a disease. However, under the careful care of its owner, it not only survived but also partially regained its tail. Additionally, some wild fish species (such as crucian carp and carp) can continue to live after their tails are lost once the wounds heal.
Limitations of Survival Ability
Reduced Mobility: The tail is the main source of propulsion for a goldfish to move in the water. A goldfish without a tail will lose its balance and have difficulty swimming normally. It may even end up with its head facing down and its tail facing up.
Vulnerable to Attacks: A goldfish that has lost its tail is more likely to become the target of predatory fish in the water because its limited mobility makes it difficult for it to escape.
Increased Risk of Disease: The absence of a tail may lead to wound infections or other health problems, which further threaten the survival of the goldfish.
The Possibility of Recovery
With proper care, the tail of a goldfish may partially recover. For instance, through medication treatment and the attentive care of its owner, a goldfish grew back a part of its tail. However, the possibility of a full recovery is low, especially for fish in the wild environment.
The Miracle of Survival
The vitality of goldfish is extremely tenacious. For example, a goldfish that was flushed down the toilet not only survived after a long journey but also grew fat and large in the natural environment. This shows that even when faced with severe physical damage, a goldfish may still survive due to its tenacious vitality.
Conclusion
A goldfish can still survive without a tail, but its survival ability and quality of life will be significantly affected. In an artificially raised environment, with careful care, the tail of a goldfish may partially recover. In the wild environment, however, a goldfish that has lost its tail faces greater survival challenges.