Today, we’ve constructed vast and expensive government bureaucracies to draw these lines. Kentucky, for instance, has outlined a number of exemptions to its new requirements that able-bodied Medicaid beneficiaries must work and pay small premiums. Former foster care youths and pregnant women don’t have to pay insurance premiums. The evicted and the homeless won’t be locked out from coverage if they miss their payments. People who are “medically frail” with serious ailments can postpone their work requirements with a doctor’s note.

Such exemptions sketch new definitions of who is truly able. And they erect more elaborate barriers to assistance as another way of winnowing out the unworthy. Eighteenth-century English overseers tried establishing rules (“nobody who tipples in the alehouse will get poor relief”). Requirements today that the poor take drug tests or pay $1 monthly premiums effectively do the same: “If you can’t figure out who is or isn’t deserving,” Ms. Ottaway wrote in an email, “then you can make rules about behavior that will force the poor to reveal themselves as worthy or not.”

By narrowing aid, proposals like Kentucky’s — and Indiana’s Medicaid work requirement, approved Friday — reverse the more recent history in which Medicaid has steadily expanded access. The program began in 1965 with Elizabethan notions intact. It initially served the elderly poor, the blind and the disabled, as well as pregnant women. Over time it came to cover more parents and children. Eligibility was extended to poor women with breast or cervical cancer. In the 1990s, some states began offering coverage on a broader basis — simply according to income.

In 2010, the Affordable Care Act sought to make that policy experiment universal. It required all states to expand coverage to everyone earning below or just above the poverty line. (The Supreme Court later made the change optional, so now 32 states and the District of Columbia have chosen to expand.) Millions of nondisabled adults have joined the program in recent years, driving down the rate of Americans without health insurance and increasing Medicaid’s ranks.

“It’s a clear sequence from 1965 to 2010, where ‘able-bodiedness,’ ‘worthy poor’ is being written out of the statute,” said Leonardo Cuello, the health policy director at the National Health Law Program, a legal advocacy group that is bringing a lawsuit against the Kentucky Medicaid proposal. “And that comes to its full completion in 2010, where able-bodiedness is explicitly irrelevant.”

For Medicaid advocates like Mr. Cuello, the recent focus on the able-bodied feels like an anachronism.

To others who use the term, it captures how Americans of both parties feel about poverty today. In one 2016 survey by the American Enterprise Institute and The Los Angeles Times, 87 percent of people said it’s better to require people to seek work or participate in a training program “if they are physically able to do so” (9 percent countered that it’s better to give the poor benefits “without asking for any effort in return”).