I think for me, it's mostly a matter of figuring out who I think they are as a person, based on their canon characterization, and then trying to write that person reacting to whatever the new situation is. If it's really far off from where they are in canon, you might need to connect the dots for the reader a little bit, either by outright explaining it (e.g. "Sorry, I used to be a lot more social, but I've been living alone in this cave for the last 30 years ...") or by trying to connect it to familiar aspects of their canon characterization in subtle ways - they might be acting different, but you, as the writer, can provide them with opportunities to bring out the "canon" aspects of their personality occasionally (e.g. if the character is usually a jokester goofball in canon, but you're writing them in a tragic scenario, you can still occasionally give them an opportunity to laugh or make others laugh, so the reader can see those canon aspects of their personality shining through).
In my last couple of fandoms, I've been writing characters who are jerks or actually downright villains in canon and putting them in situations that bring out a softer, friendlier side we rarely saw, but I still try to give them plenty of openings to actually be a jerk, or be violent, so they don't come across too soft and "reformed" to be in character -- there is a whole lot of backsliding even though they're trying to be better. So that might be useful in the scenario you're writing -- either by showing that he is still like that in some ways, or by putting him in a situation that previously would've led to violence and showing that he's changed by having him back down and turn away from it.
(Think, say, that scene in the Back to the Future movies when Marty-at-the-start-of-the-movie would've accepted a challenge to drag race that might have resulted in getting hurt or killed, because he didn't want people to think he was a coward, but at the end of the movie he's put in that situation and turns it down. It's a useful trick in fanfic, too. You can put your character in a situation very similar to something they encountered in canon, and have them make a different choice, while at the same time recognizing that the "old" them would've done the other thing.)
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In my last couple of fandoms, I've been writing characters who are jerks or actually downright villains in canon and putting them in situations that bring out a softer, friendlier side we rarely saw, but I still try to give them plenty of openings to actually be a jerk, or be violent, so they don't come across too soft and "reformed" to be in character -- there is a whole lot of backsliding even though they're trying to be better. So that might be useful in the scenario you're writing -- either by showing that he is still like that in some ways, or by putting him in a situation that previously would've led to violence and showing that he's changed by having him back down and turn away from it.
(Think, say, that scene in the Back to the Future movies when Marty-at-the-start-of-the-movie would've accepted a challenge to drag race that might have resulted in getting hurt or killed, because he didn't want people to think he was a coward, but at the end of the movie he's put in that situation and turns it down. It's a useful trick in fanfic, too. You can put your character in a situation very similar to something they encountered in canon, and have them make a different choice, while at the same time recognizing that the "old" them would've done the other thing.)