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Poppies can be susceptible to Downey Mildew, Grey Mold, Powdery Mildew, Tomato Wilt Virus, and Rhizoctonia Root Rot.
Without seeing the plants or leaves, and the time of year, I would suspect a fungus disease of some type.
Clean up and dispose of any dead leaves to prevent spread of disease.
Avoid water splashing onto the leaves with overhead watering and apply a fungicide to the remaining plants on a cool, overcast day.