The answer depends on the person’s reason for not reconciling. If the one who offended is sorry for the wrongdoing and is making sincere attempts to change, then this can make reconciliation a definite possibility. If the forgiver refuses to even consider reconciliation at this point, and if the forgiver still is showing deep anger, then it is possible that the forgiveness is either at a very early stage or is not genuine. On the other hand, if the one who engaged in the wrongdoing remains unrepentant and refuses to change the behavior, the forgiver still can forgiver deeply from the heart and not reconcile because it could be unhealthy or even dangerous, depending on how hurtful the injustice is.
For additional information see: Learning to Forgive Others.