Which system is used to support an existing structure when new excavation is below the foundation?

Underpinning is the correct choice as it specifically refers to the process of strengthening and stabilizing the foundation of an existing structure. This is particularly necessary when new excavations are made below the foundation, which can compromise the structural integrity of the building. Underpinning involves extending the foundation deeper or distributing its load over a larger area, ensuring that the building remains stable during and after the excavation.

In contrast, piling primarily involves driving structural supports into the ground to provide a foundation for new structures rather than supporting existing ones. Cribbing and tie-backs may provide temporary support or lateral stabilization but are not specifically designed for deep foundational support beneath existing structures. Cofferdams are typically used in water environments to create a dry work area for construction, which does not directly involve underpinning. Each of these options serves specific purposes in construction, but underpinning is uniquely suited for the scenario described in the question.