According to the Work Permit Conditions, a foreign domestic worker (FDW) is allowed to work only for the employer at the residential address stated on the Work Permit. This is to prevent FDWs from being exploited into working for multiple households and employers.
Your relative will have to be the official employer if they require an FDW.
If your relative is unable to meet the existing criteria for employing an FDW, they can consider applying under a special scheme such as the Joint Income Scheme or Sponsorship Scheme.