I'm not sure about what happened to a person who was exiled in Japan, but I feel there are some things that can be cleared up first. In the FAQ there is this about seppuku by /u/ParkSungJun: https://www.reddit.com/r/AskHistorians/comments/27vhc1/how_common_was_seppuku_japanese_ritual_suicide/ci4sa05/

You also mention "Bushido" which /u/bigbluepanda and /u/ParallelPain talk about here: https://www.reddit.com/r/AskHistorians/comments/52sewz/was_the_way_of_bushido_ever_documented_in_a_book/

One thing I think you can take away from the answer /u/bigbluepanda gives is,

"The main thing to take away is that there is no universal "code" that somehow ran through the lineage of samurai starting from the early 11th centuries all the way through to the Meiji and onwards - whatever loose philosophies that could be considered any kind of 'code' dealt more with duty, responsibility, and loyalty, than what we take today as being bushido. Not only this, no one would have hesitated in breaking said 'code' if it meant they could see more benefit for themselves."

So, a samurai who broke "the code of Bushido" probably wouldn't commit seppuku anyways, not unless the offense he committed was something bad enough that someone could force him to commit seppuku.

Seppuku is a punishment for concrete offenses, or suicide to prevent capture when a battle is lost. There's also cases of voluntary seppuku, but obviously they don't factor in here, and no one would bat an eye if you didn't, because in these cases you did it because you wanted to.

If you were ordered to commit seppuku and didn't, or lost a battle but didn't want to commit seppuku, you can try running away and hiding to save your own life. If you're captured, or was already under custody, they'll just execute you. In this case seppuku is a privilege for members of the samurai class to try to retain some social/political/economic standing for their family despite a death sentence. If you pass up on that privilege, you'll just be executed like a common criminal.

However, if you do have powerful friends to beg your life for you, they might be able to downgrade your sentence to exile. This would obviously take place long before you are on your knees ready to cut your belly. Should you be so fortunate, the likely location of your exile would be one of the tiny, remote islands of the Japanese archipelago like Hachijōjima, Iōjima, the Oki Islands, or Ezochi (modern Hokkaido, then not under control of Japan). If you were really fortunate, or if you lived in the Sengoku when no one really had enough control to send you to these places, you'd be forced into a monastery to live out the rest of your life as a monk, or exiled to a remote village (likely close to or as part of a monastery) for the same. Who knows, you might even be pardoned later.