An elderly woman who is permanently unable to perform Hajj — due to old age, chronic illness, or physical disability that prevents travel — may appoint a proxy (na'ib) to perform Hajj on her behalf. This is agreed upon by all four schools of jurisprudence and is based on the explicit hadith where a woman asked the Prophet about Hajj for her elderly father who could not sit firmly on a mount, and the Prophet permitted proxy Hajj.
Sheikh Ibn Baz stated that the condition for appointing a proxy is that the inability must be permanent — the person must have no reasonable expectation of recovery. Temporary illness does not justify proxy Hajj; the woman should wait until she recovers. If the elderly woman has the financial ability but cannot physically perform Hajj, the obligation remains and must be fulfilled through a proxy. She should pay for the proxy's expenses from her own wealth.
Sheikh Ibn Uthaymeen clarified that the proxy may be male or female, and should have already completed their own obligatory Hajj. The proxy makes the intention specifically on behalf of the elderly woman at the miqat: 'Labbayk on behalf of [her name].' The proxy performs all the rites exactly as they would for their own Hajj. If the elderly woman passes away before a proxy is sent, her heirs should arrange for proxy Hajj from her estate if she had the financial means during her lifetime.