Answer: Based on your description I am not certain what is happening to your yucca. None of the common pests on yucca quite match your described insect. I suspect there may be a disease bothering the foliage and then the insect is attracted to that. It might be a fungal problem, for example. I would strongly suggest you consult with your local county extension to obtain a specific diagnosis of the problem and identify the insect you are seeing, and then based on knowing that, decide how to proceed. If it is something that can be controlled with a spray, they will tell you exactly what product to use and how/when is best to apply it. I'm sorry you are having trouble with your plant.
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