Then they are eligible for Medicaid, the state-run safety net for the poor. While Medicare, a federal program, is financed by payroll taxes, and thus is an “earned” benefit, Medicaid is “charity,” in the minds of the formerly middle class who worked their whole lives and never imagined themselves destitute.

In the case of my mother, who died at 88 in 2003, room and board in various assisted living communities, at $2,000 to $3,500 a month for seven years, was not paid for by Medicare. Yet neurosurgery, which I later learned was not expected to be effective in her case, was fully reimbursed, along with two weeks of in-patient care. Her stay of two years at a nursing home, at $14,000 a month (yes, $14,000) was also not paid for by Medicare. Nor were the additional home health aides she needed because of staffing issues. Or the electric wheelchair after strokes had paralyzed all but the finger that operated the joy stick. Or the gizmo with voice commands so she could tell the staff what she needed after her speech was gone.

She paid for the room. My brother and I paid for the private aides and bought her the chair and the “talking board.” What would her life have been like without the skilled care she required and the ability to get around her floor and communicate her needs? I shudder to think. But none of this was Medicare’s responsibility.

Yet Medicare would pay for “heroic” care for a woman who was dying of old age, not a disease that could be treated: Diagnostic tests. All manner of surgery. Expensive medications. Trips to the emergency room or the hospital — had she not refused all of them, in the last year of her life. So, in less than a decade, by my low-ball estimate, my mother spent $500,000 of her own money and uncalculated sums from her two children before winding up what she considered, with shame, “a welfare queen.”

A recent state-by-state study of long-term care, the first of its kind, by a consortium of researchers, has found that this kind of essential help costs anywhere from 166 percent to 393 percent of the average annual income of America’s elderly.

BY now, you may be wondering if your parents have a half million dollars for old age. Or if you or your children do. You may be counting on quick and easy deaths. Shoot me, so many people say. Alas, 70 percent of the elderly will need extended care before they die. Denial is powerful but doesn’t pay the bills.

This mismatch between what is covered and what is actually useful is the central flaw in Medicare today, a shock to families who have no clue, until they’re smack in the middle of it, about how this system works.