Elation overcame Andrei Kuznechyk when he was freed in February after three years in a Belarus prison on charges of leading an “extremist organization,” the authoritarian government’s byword for his work as a web editor at the Belarus service of Radio Free Europe/Radio Liberty.

Pangs of sadness soon followed. He said he realized, after being blindfolded, driven to the border and handed over in a deal orchestrated by Washington, that he may never return to his homeland, Belarus, again. When he reunited with his 5-year-old son, the boy did not remember him.

And after Mr. Kuznechyk, 47, arrived in Lithuania to live in exile, the president of the U.S.-funded news media outlet took him to buy new clothes (he had lost more than 30 pounds in prison) and relayed some difficult news: Radio Free Europe/Radio Liberty may close.

Mr. Kuznechyk had worked for more than a decade at the outlet, which began broadcasting in the early 1950s behind the Iron Curtain. The organization has long coped with challenges from authoritarian governments while reporting on human rights and corruption. Now, for the first time, the biggest threat is coming from Washington.

A month after his administration secured Mr. Kuznechyk’s release, President Trump issued an executive order demanding the dismantling of the outlet’s parent organization, the U.S. Agency for Global Media, through which Radio Free Europe/Radio Liberty receives funding from Congress.