There are a variety of products that are available to help cover the costs of nursing home care, assisted living care and Alzheimer's care. These products range from Long Term Care insurance to Life Insurance as well as hybrids of the two.
You can always try to "self-insure" and save the money you might need - but it can be a LOT of money.
Understand that until you are in a Skilled Nursing Facility (more like a hospital than a place most folks want to be), Medicare does NOT cover any of those costs so you or your family will have pay for your care when you get too old and sick to care for yourself.
There are loads of variables from family history to your sex to how well you have taken care of yourself (or your spouse). Planning for this should be done with the help of an expert, preferably a CFP® professional who can balance this issue with all the other moving parts to your personal financial life.