The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at You Know, That Thing Where.
^Going Native is by choice. The OP means when the captive is forced to comform to their captors' way of life.
I think the The Last Samurai example is still textbook Going Native, even if the subject was forced at first, especially since the change was one of culture rather than morality.
The next step up in terms of "forcible conformance" would be Stockholm Syndrome or Being Tortured Makes You Evil, which would apply to being captured by a group that is unambiguously bad (e.g. hostage-taking criminals or The Empire).
Edited by KD
There's a trope in a few movies; like The Last Samurai, where the protagonist is captured by the enemy and forced to learn their ways. After a while, the protagonist might side with them, even though they gain the option to go free. Can someone link me to this trope or where I can find more examples of it? Thanks.