```ts
export interface User {
  email: string;
  active?: boolean; // Optional property
}

/** The lowercased addresses of the active users, in order. */
export function activeEmails(users: readonly User[]): string[] {
  return users
    .filter(user => user.active === true || user.active === undefined) // Include inactive or missing 'active' as false
    .map(user => user.email.toLowerCase());
}
```