Forgiveness should never be "obligatory".
It would all depend on the circumstances whether I make a choice to extend forgiveness to someone. If, as you mentioned, they show no remorse and don't even seem to comprehend how their actions were so seriously harmful to you, and they are only interested in having you forgive them so they can re-abuse you all over again, then NO, I do not feel that would be a healthy way to extend forgiveness.
Forgiveness is a gift I give to myself, not necessarily to the person who wronged me in the first place. It is giving myself permission to let go of that incident and to move forward and stop allowing the incident to be a focal point of my existence.
I really don't feel any compulsion to contact people who have harmed me and let them know that I'm not allowing their abuse to consume my energy any longer. The fact that they are not in my life anymore and make no effort to have them there is their loss, not mine. It is a consequence of their choice to deal with me the way they did.