TYLER, Ala. — The hard clay soil in this rural Southern county has twice cursed Dorothy Rudolph. It is good for growing cotton and cucumbers, the crops she worked as a child and hated. And it is bad for burying things — in particular, septic tanks.

So Ms. Rudolph, 64, did what many people around here do. She ran a plastic pipe from her toilet under her yard and into the woods behind her house. Paying to put in a septic tank would cost around $6,000 — a little more than half of her family’s annual income.

“It was a whole lot of money,” she said. “It still is.”

Here in Lowndes County, part of a strip of mostly poor, majority-black counties that cuts through the rural center of Alabama, less than half of the population is on a municipal sewer line. While that is not a hardship for more affluent communities — about one in five American homes are not on city sewer lines — the legacy of rural poverty has left its imprint here: Many people have failing septic tanks and are too poor to fix them. Others, like Ms. Rudolph, have nothing at all.

That is not so uncommon. Nearly half a million households in the United States lack the basic dignity of hot and cold running water, a bathtub or shower, or a working flush toilet, according to the Census Bureau. The absence has implications for public health in the very population that is the most vulnerable.