In the case of the US, the story of Joseph Beyrle,a German American has been very well documented and is an amazing one.

Disclaimer: I am not a professional historian, but I have just finished reading Thomas.H Taylor's book on this topic.

Joseph Beyrle, was a paratrooper fom the 506th PIR in the 101st Airborne who specialized in demolitions and communications. He was also a very competent jumper, having done many proxy jumps for other paratroopers in training. For this , he performed 2 combat jumps into occupied France before D-Day for delivering gold to the French resistance, making history as the first American paratrooper to parachute in France.

On D-Day , his plane was shot and he became separated from other paratroopers. He blew up a power station before he was captured by German paratroopers. He escaped the next day and was captured again. He was then taken to Germany and put in 7 different prisons and before being taken to Stalag III. (He was incorrectly listed as KIA, in the US Army records.)

In January 1945 he escaped from the camp and linked up with approaching Soviet unit commanded by a female tank commander(Major Aleksandra Samusenko). With the Soviets he fought till he was wounded near Kustrin in the same month.

He was evacuated to a Soviet hospital in Poland, where Zhukov visited and gave him a "passport". Using which he went to the American embassy in Moscow, where he was initially suspected to be a Nazi assasin, (due to him being listed as KIA in the records) and after a lot of cross checking he was officially identified .

In 1994 he was awarded medals from both USA and Russia.

Source: Behind Hitler's Lines , Thomas H Taylor