Final answer:
Hospice care is focused on providing comfort and support to terminally ill patients in a homelike setting, often including at-home care, and benefits both the patient and their families.
Step-by-step explanation:
The care described as involving a small number of patients and specially trained healthcare workers in homelike settings is known as hospice care. This type of care is for terminally ill patients when cure-oriented treatments are no longer viable. Hospice care focuses on comfort and peace at the end of life rather than on curing the illness. It provides support not only to the patient but also to the family by reducing the burden of care and improving emotional and social support. This approach also includes at-home care, allowing patients to spend their last days in a familiar environment surrounded by loved ones. Increased patient and family satisfaction, extended lifespans for hospice patients, and reduced healthcare costs underscore the benefits of hospice care.