He began to keep a journal and was 'faithful to' it for years. [=he continued to write in his journal for many years]
The movie is 'faithful to' the book. [=the story told in the movie closely matches the story told in the book]
He was not 'faithful to' his word. [=he did not do what he said he would]
(..) The choice is yours, Scar. Either step down or fight. Wouldn't you agree, Simba? That's not gonna work, Scar. I've put it behind me. Eh, but what about your faithful subjects? Have they put it behind them? Simba, what is he talking about? Ahh, so you haven't told them your little secret. I am. (..)1994 The Lion King