It depends on the circumstance. But generally, you move on.

I agree it depends on what happened, but it takes fortitude to admit being wrong. Unless the other person is an absolute jerk about admitting it, take it as a start. It doesn't mean there isn't a certain amount of growing back into a relationship, and you don't have to hug everything out and forget it right away.

Far too generic of a LPT as it will depend on the context of what happened, how they admitted they were wrong etc

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What should I do or what should you do?

This is far too dependent on the context to be at all helpful. Sometimes what they might consider a “punishment” is you setting healthy boundaries. You have every right end relationships if needed and protect yourself and your own well-being.

Always forgive, but that doesn’t mean things go back to the way they were. But like I said, each situation is so wildly different.