This is deliberate and it is a test of composure, not a mistake on their part.
Do not panic or start over. Say what the change breaks, then adapt the smallest part possible.
Worked example. You designed a single-region URL shortener; 25 minutes in they say "now users are global."
- Acknowledge the impact. "That breaks my single-primary assumption, because writes from Asia would pay a 200 ms round trip to a US primary."
- Identify what survives. "The data model, hash generation and cache strategy are unaffected."
- Change only what must change. "I will add regional read replicas plus a CDN for redirects, since redirects are read-only and cacheable. For writes, I will pre-allocate disjoint key ranges per region so each region can generate short codes locally with no coordination."
- State the new trade-off. "A newly created link may take a second to be visible in another region. For a URL shortener that is acceptable."
Interviewers add requirements specifically to see whether your design has clean seams. A design that must be rebuilt from scratch was too tightly coupled.