Stephanie Douglas signed up for health insurance in January with the best intentions. She had suffered a stroke and needed help paying for her medicines and care. The plan she chose from the federal insurance exchange sounded affordable — $58.17 a month after the subsidy she received under the Affordable Care Act.

But Ms. Douglas, 50, who was working about 30 hours a week as a dollar store cashier and a services coordinator at an apartment complex for older adults, soon realized that her insurance did not fit in her tight monthly budget. She stopped paying her premiums in April and lost her coverage a few months later.