Physical violence cannot be undone.

Neither can emotional manipulation. You cannot see the scars, but they will bear a violent fruit.

Saying that you want to leave someone, and then breaking down upon noticing your mistake is something that can be talked through.

Don't be a doormat for emotionally unstable people. There can be a conversation, a couple counseling or something, when people talk to each other. Putting signed divorce papers in the other persons hand is a gesture, not a conversation. There is nothing left to be said.

If someone beats you, and says it was an accident, you'll still be bruised and feel unsafe around them, even if you understand them and have empathy for them.

Yes, trust can easily be broken by physical violence. It can also be broken by the spoken or written word.

On the other hand, if you understand and have empathy for a partner that said they would leave you because they honestly though you would be happier without them, you can help them get better and move on.

Oh, it sounded like the husband would be responsible for her mental health, but this is about helping? Then yes, you can help someone get better. If she works on herself to get better you can help her.

Just like you can help a veteran with PTSD. If they work on themselves so they can get better.