Yes, it is possible to forgive even if reconciliation is not possible. You can see the person as possessing inherent worth. You can feel some compassion for the person as a person, even in his or her weaknesses. Even if you have some anger left over, this does not mean you are unforgiving. People can forgive, reduce resentment, and still have some anger. As long as that anger is not dominating you and you are in control of that anger, you can be forgiving.