Short answer: Usually not. Medicare and most health insurance pay only for skilled, short-term care, not the ongoing personal help, like bathing, dressing, and eating, that makes up most long-term care.
Medicare covers a skilled nursing facility stay only for a limited time (up to 100 days, and the average covered stay is far shorter) and home care only when you also need skilled services. It does not cover custodial care, meaning help with bathing, dressing, eating, and similar tasks when that is the only care you need. Most health insurance plans follow the same limits.
That gap is why long-term care is treated as its own planning problem. If you expect to need ongoing personal-care support, you generally cannot rely on Medicare or a standard health plan to pay for it, and should look at Medicaid eligibility or private options such as long-term care insurance.