We initiate that process by deciding that we want to forgive. But that process is completed when we, through a gift from God, no longer feel ill will toward the person who injured us. At the same time, the old feelings of pain no longer rush back at us, when we remember the injury. We are at peace with that person and that memory. Forgiveness is a one person act.
Reconciliation is a two person act, which requires the full cooperation of the injurer.
Forgiveness is complete in itself in one person, even if the injurer chooses not to respond in such a way that reconciliation is a possibility. Sometimes it is necessary for them to build that self-esteem back up, before they can really forgive the one who injured them. I often cite Joseph as an example of this. Clearly, Joseph did not know how to react to his brothers when they appear before him. He therefore tests them and it is only after Judah's emotional appeal when the cup is found in Benjamin's sack, that Joseph can be certain that the brothers have had a change of heart and are truly sorry for what they did to their brother and the suffering that their actions inflicted on their father.