Yes, kimchi can become over-fermented if left at room temperature for too long, resulting in a sour taste and mushy texture. While it doesn't necessarily 'spoil' in the traditional sense, it can become unpalatable.
Kimchi fermentation is driven by lactic acid bacteria (LAB). These bacteria consume sugars in the vegetables and produce lactic acid, which gives kimchi its characteristic sour and tangy flavor. When kimchi is fermented at room temperature, the LAB become very active. If left for too long, they will continue to produce lactic acid, leading to a very sour or acidic taste. The texture can also change, becoming softer and mushier as the bacteria break down the vegetable fibers. While over-fermented kimchi is still safe to eat (unless mold grows), the flavor and texture may be undesirable. The ideal fermentation process involves an initial period at room temperature to kickstart the fermentation, followed by refrigeration to slow it down and preserve the kimchi at its peak flavor. The length of time at room temperature depends on the ambient temperature; warmer temperatures will accelerate fermentation.
If your kimchi becomes too sour, you can still use it! Incorporate it into dishes like kimchi jjigae (kimchi stew), kimchi fried rice, or kimchi pancakes to balance the sourness with other flavors. The cooking process can also mellow out the intense sourness.