What is the ruling on the maid, whom my grandmother raised, remaining in my grandfather's house to serve him after my grandmother's death, knowing that my grandfather is 75 years old and lives alone?

A man is not permitted to be alone with a non-mahram (definition) woman, even if he is an old shaykh. This is based on the Prophet's (peace and blessings be upon him) saying: "No man should be alone with a woman, and no woman should travel except with a mahram." The majority of jurists believe that Satan becomes the third party in such a situation. Your grandfather, who needs someone to serve him, can avoid unlawful seclusion by choosing one of the following options: marrying the woman who serves him, having one of his children or grandchildren serve him, having another person present with him during the maid's presence, or having the maid work while he is outside the house.