Final answer:
The approach to caring for terminally ill patients that focuses on comfort and individual preference, often in a home setting, is known as hospice care.
Step-by-step explanation:
The approach to caring for the terminally ill that focuses on individual and family control over the process of dying is known as hospice care. Hospice care enables terminally ill patients to spend their last days in a comfortable, familiar environment, usually outside of a hospital. The goal of hospice is to provide death with dignity and effective pain management. This type of care emphasizes comfort and quality of life rather than curative treatments. Additionally, this approach supports the emotional and psychological needs of both patients and their families during the end-of-life process.