During the US campaign in Vietnam, over a thousand service members were classified as prisoners or war (POW) or missing in action (MIA.
Generally, those who went missing were killed or captured by the North Vietnamese.

But in a few instances, as Robert Beckhusen recounts at War is Boring, Americans were captured or went MIA when their planes were shot
down in or near Chinese airspace. Beijing's role in the conflict is becoming increasingly apparent as the NSA releases signals intelligence (SIGINT)
documents from Vietnam and Southeast Asia.

For instance, on September 20, 1965, US Air Force Captain Philip E. Smith accidentally flew over the Chinese island of Hainan after his navigation
equipment stopped working and he became lost in heavy cloud cover. A Chinese MiG-19 intercepted and shot down Philips due to his violation of Chinese territory. ...