```ts
export interface User {
  email: string;
  active?: boolean; // Changed from 'boolean' to '? boolean' for optional property
}

/**
 * The lowercased addresses of the active users, in order.
 */
export function activeEmails(users: readonly User[]): string[] {
  return users
    .filter(user => user.active !== false) // Filter out inactive users by checking falsy values
    .map(user => user.email.toLowerCase());   // Map to lowercase and collect results
}
```