This is no movie, however, and the former world chess champion is in a real bind, appealing Japan's decision to deport him to the United States and hoping a third country will grant him asylum.
Japan has been holding Fischer at Narita Airport since last week, when he tried to board a flight to the Philippines with an invalid passport.
Fischer - who became an American icon and Cold War hero when he beat Russia's Boris Spassky in Iceland in 1972 - has been a different man in the past few decades and is wanted on charges in the U.S.
Miyoko Watai, of the Japan Chess Association, a longtime friend, says Fischer is now trying to hire a lawyer to help him find a third country to take him in.
"There is no other way," says Watai. "Otherwise, he will be sent back to the United States."
Watai also says Fischer is "a pathetic sight" in custody.
Fischer, 61, was detained by Japanese immigration officials last week after trying to leave the country for the Philippines.
Fischer is wanted in the United States for playing a rematch against Soviet world champion Boris Spassky in Yugoslavia in 1992. Yugoslavia was under international sanctions at the time, and U.S. citizens were banned from doing business there.
Fischer won the match and more than $3 million in prize money.
Believed by many to be the greatest chess player ever, Fischer became U.S. chess champion at age 14, and a grandmaster at 15.
His genius for chess has been overshadowed by increasingly bizarre behavior that among other things, caused him to lose his world champion title back in 1978. After that, he for the most part vanished from the public eye.
Over the years, Fischer gave occasional interviews with a radio station in the Philippines, often digressing into anti-Semitic rants and accusing American officials of hounding him.
He praised the Sept. 11 terrorist attacks, saying America should be "wiped out," and described Jews as "thieving, lying bastards." His mother was Jewish.
Fisher has lived in seclusion and semi-secrecy for decades. It remains unclear where he considers home, but after he was taken into custody, friends here said he frequently traveled, staying for short durations in Japan, the Philippines, Germany and other countries.
He is believed to have been in Japan since about April.
Immigration officials have refused to comment on Fischer's case, other than to confirm he was taken into custody and faces deportation. When that might happen remains unclear. Requests by The Associated Press to meet with Fischer have been denied.
"It is a race against time," says Watai. "We are fighting this from morning to night."