Do poinsettia leaves curl when the plant is dying?

No, the leaves do not curl just when poinsettias (Euphorbia pulcherrima) are dying.

Specifically, there are poinsettias that have been cultivated to grow curling leaves. Otherwise, poinsettias curl leaves to indicate stress. Usually that stress reflects the presence of ethylene or incorrect watering. Ethylene is produced when poinsettia leaves are forced upwards, such as when they are wrapped for transport.

In terms of watering, poinsettias require soil that never dries and never is water-logged. Leaves particularly will start curling when the plant's soil is allowed to dry out between waterings. After the bloom and until new growth, the plant's soil may be allowed to dry slightly out - but without showing cracks and fissures - about 1 inch/2.54 centimeters down from the surface, between waterings. During that time period, the plant should continue to be watered every 10 days.