It has 4 leafing branches, 2 of which are fine but the other 2 appear to be wilting and have softer stems.
A Yucca Plant
Certified GKH Gardening Expert
It sounds as if the Yucca is unhappy in it's growing conditions.
Full sun and dry soil are key factors.
Watering should only be when the top 3 inches of soil are dry.
Water should not hit the leaf branches.
Also good air circulation will help in plant health.
A stressed and overly watered can become diseased with fungus or insects.
Allow the plant to dry. You can apply a fungicide and treat with Neem Oil if any signs of insects.
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