```ts
export function traceRelay(links: Record<string, string>, start: string): string[] {
  if (typeof links !== 'object' || links === null) {
    throw new Error('links must be a non-null object');
  }
  if (typeof start !== 'string') {
    throw new Error('start must be a string');
  }

  const visited = new Set<string>();
  let current = start;

  while (current !== '') {
    if (!visited.has(current)) {
      visited.add(current);
    } else {
      throw new Error('handoff loop detected');
    }
    current = links[current];
  }

  return Array.from(visited);
}
```