The type of insurance primarily designed to cover nursing home or in-home care expenses is called:

Disability income insurance provides financial support in the event that an individual becomes unable to work due to a disabling condition. While it can be essential for income replacement, it does not cover the costs associated with long-term care services, such as those provided in nursing homes or through in-home assistance.

Medicare supplement insurance, or Medigap, is intended to cover the out-of-pocket costs that Medicare does not pay, such as copayments, coinsurance, and deductibles. It does not provide coverage for long-term care services, which are often not included in standard Medicare plans.

Major medical insurance is designed to cover high-cost medical expenses, such as hospital stays and surgeries, but it typically does not cover long-term care services. This type of insurance mainly focuses on acute medical needs rather than ongoing care requirements associated with chronic conditions.