Assuming you cannot self-insure, the best available solution for this scenario is a combination of what's called "long-term care insurance" (LTC insurance) and medical insurance. Medical insurance typically covers acute care hospitalization expenses that are typical of long-term care patients. (Integrated Shield plans, optionally with riders, are the most common medical insurance policies in Singapore.) LTC insurance helps support daily living if you meet the policy's disability standard, usually a "3 of 6 Activities of Daily Living" (ADL) standard.
ElderShield 400, and the ElderShield Supplements, are a form of LTC insurance. You must purchase ElderShield by age 70, and preexisting conditions are not covered. Premiums are payable using Medisave, so for this reason it's probably the most attractive available LTC insurance in Singapore. If you are a CPF member, you are enrolled automatically in ElderShield 400 when you turn 40, and you have to opt-out if you don't want to be enrolled. You also have to take action if you want more than the $400/month benefit level.
Unfortunately ElderShield payouts are capped at 72 months, and that's not a terrific feature. There are nontrivial numbers of patients who meet the 3 of 6 ADL standard and who live longer than 72 months, sometimes much longer.
Starting at age 65 (as early as) you will also presumably have a CPF LIFE annuity income stream. You may be able to increase that annuity, defer it (to age 70), and/or opt for the 2% annual increase payout option. Income and wealth are always useful to pay for expenses, including nursing home and home care expenses. This is part of your "self insurance."
If you have no dependents then you do not need life insurance, which is a different insurance product than LTC and medical insurance products.
