Caribbean copper plant (Euphorbia cotinifolia) is a tropical succulent hardy only to zone 10 (30°F minimum). "Deciduous" means it drops leaves in drought/cold—not that it survives freezing. A Los Angeles freeze likely killed it.
Test: scratch bark with fingernail. Green cambium = alive; brown = dead. If alive, fertilize lightly, water sparingly, wait. If dead, replace with a hardy alternative like purple hopseed bush (Dodonaea) or smoke tree (Cotinus).
Future: grow in containers, move indoors below 40°F. Or choose truly hardy plants for your zone.
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