“They want everything to be controllable, and if he went abroad, he would lie beyond their control,” Cui Weiping, a retired professor of Chinese literature and friend of Mr. Liu, said from Los Angeles, where she now lives. “This has always been the purge approach for dealing with dissidents — minimize their influence so they don’t become a focus.”

Image A picture shared on Twitter by the activist Ye Du showing Mr. Liu and his wife, Liu Xia. Credit... Ye Du, via European Pressphoto Agency

Yet while the government wants Mr. Liu to stay silent and to ensure that his legacy fades as quickly as possible, his supporters have mobilized, despite intense restrictions and police warnings. They want to win him the right to speak out, go abroad for palliative treatment and decide how he is memorialized.

Some sympathizers of Mr. Liu have tried to visit him in his hospital, where the police blocked their way; some organized a petition calling for him to be given freedom at the end of his life. Longtime friends of Mr. Liu have been warned not to speak out or placed under police watch, including Zhou Duo, a scholar who joined Mr. Liu on Tiananmen Square on June 3, 1989, as armed soldiers closed in, when they and two other friends negotiated the safe passage of protesters who were still there.

“To make Liu Xiaobo spend his final time like this doesn’t bring honor to the government, but they’ll stick to their ways,” said Wen Kejian, a friend of Mr. Liu who unsuccessfully tried to visit him in the hospital. “I think the chances that we’ll get what he wants are slim — that would require a dramatic change in the system — but we must try our best.”

Mr. Liu, 61, was moved from prison to the First Hospital of China Medical University in Shenyang, 390 miles northeast of Beijing, last month, and officials revealed that his cancer had already reached a terminal stage. Mr. Liu has said that he wants to travel to Germany or the United States for treatment. The Chinese government has not flatly rejected that request, but it has left little hope it will say yes.

But by keeping Mr. Liu locked up as he dies, the Chinese government has soiled its own image, said Liao Yiwu, an exiled Chinese author living in Berlin who knows Mr. Liu. Domestic Chinese news reports about Mr. Liu are heavily censored, and his illness has gone virtually unmentioned, except in English-language outlets read by few. But the images of Mr. Liu, gaunt on a hospital bed, have caused anger and disgust in China among the small minority who have seen them, Mr. Liao said.

“By locking him up and preventing him from traveling abroad, they’re actually making him even more symbolically powerful,” Mr. Liao said by telephone. “Now the whole world is paying attention, and I think that’s even more powerful.”