When soldiers shot at pro-democracy protesters on June 4, 1989, one of the casualties was Qi Zhiyong, then a young construction worker who had come to Tiananmen Square out of curiosity. Bullets hit both of his legs, one of which was later amputated. He received a bad blood transfusion that gave him hepatitis C, and in recent years his kidneys have failed. Now 63, Mr. Qi spends three days a week in a Beijing hospital bed, receiving dialysis treatment.

Despite his frailty and age, the authorities still regard him as a “sensitive...