How do Buddhists talk about forgiveness and turning the other cheek, for extreme wrong doing?
one may be happy to let karma do its job
Recalling the brahmaviharas, I think that that -- i.e. &quot;remembering that beings are heir to their own karma&quot; -- is recommended as a recipe for &quot;equanimity&quot;.
That's possibly not &quot;good will&quot; though -- i.e. if you're &quot;happy&quot; about someone's misbehaviour, that sounds like the opposite of mudita -- and good-will is important, see e.g. the parable of the saw (as an example of Buddhist doctrine that's relevant to what you're asking).
There's also the Dhammapada verses 3 through 6 -- which recommend against &quot;he hurt me!&quot; and &quot;not stilling your hatred&quot;...
There are other topics on this site though, about social justice -- e.g. if a person lies then you might not want to believe them in future; if they steal you might tell the police...
Or one of the Zen stories is The Thief Who Became a Disciple

I gave him the money and he thanked me for it.