Final answer:
After fertilization, the sepals of a flower are the parts that typically do not dry up or fall off, whereas the stigma, style, and petals often do. Sepals might persist to protect the developing seed or fruit.
Step-by-step explanation:
After fertilization, the part of a flower that typically dries up or falls off is the stigma, details, style, and sometimes the sepals. However, the question specifically asks which part does not dry up. In this case, unlike the highly visible features such as petals which often wither and fall away to reveal the fruit or seedpod, sepals can remain intact and continue to provide protection throughout the development of the seed or fruit.
The stamen and pistil are the respective male and female reproductive parts of the flower. The pistil, which comprises the stigma, style, and ovary, is designed to facilitate reproduction, with the stigma acting as a landing platform for pollen. Once fertilization has occurred and the seeds begin to develop, the reproductive structures have served their purpose. The petals also typically fall away as they are primarily there for the attraction of pollinators. However, sepals which initially protected the flower bud, can remain as a protective organ.