Patients with serious illnesses need medical treatments to survive. But they are increasingly taking advantage of the specialty known as palliative care, which offers day-to-day relief from symptoms as well as stress and lifestyle management.

Though often regarded as only for older patients with terminal illness before they enter hospice programs at the end of life, palliative care is increasingly being offered to patients of any age with a range of chronic illnesses such as cancer, multiple sclerosis and Parkinson’s. It may...