What type of insurance provides coverage for catastrophic or prolonged illness?

That will be long-term care insurance. It covers expenses for chronic illnesses such as diabetes, Alzheimer's, cancer, HIV/AIDS and injuries sustained from accidents and other cognitive and physical impairments/disabilities. It also pays for stays in care facilities if ever you needed one like a nursing home, assisted living, or adult day care. You also get coverage for in-home care just make sure that specified in your policy.

ANSWER:

Coverage for hospitalization and other services that focused on health care is provided by health insurance, while coverage for custodial/medicare/personal assistance and other long term care services brought about by disability, injuries and chronic illness is provided by long term care insurance (source: infolongtermcare). That includes long term care facilities like nursing homes, assisted living or even home are.