BEIJING—China says 95% of its 1.34 billion people are covered by medical insurance. That should have included Zhao Guomei, whose struggle with a rare but treatable disease shows how the system is failing for millions of China’s workers.

Doctors in July diagnosed Ms. Zhao with aplastic anemia, a bone marrow condition that put her at high risk of infection. They estimated her treatment would cost at least 400,000 to 500,000 yuan, or roughly $65,000 to $82,000.

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