Final answer:
Fibers that enter and leave the sympathetic chain without synapsing are known as splanchnic nerves, which are myelinated and project through the white ramus communicans to a prevertebral ganglion.
Step-by-step explanation:
The fibers that enter and leave the sympathetic chain without synapsing are called splanchnic nerves. These are myelinated structures that provide a path for the axon from a central sympathetic neuron in the spinal cord to the periphery, specifically through the white ramus communicans. Unlike the fibers in the white rami communicantes, which synapse at the chain ganglia, the splanchnic nerves continue to a prevertebral ganglion such as the greater splanchnic nerve or the inferior mesenteric ganglion. An example of their pathway is when a neuron does not synapse in a chain ganglion but instead projects through one of the splanchnic nerves to synapse within a prevertebral ganglion like the celiac ganglion.