When the apology is never coming and you still have to live
Forgiving someone who has never said sorry is a real and complete act in the Qur'an, worth as much as any other good you do. "Whether you do good openly or in secret, or pardon a wrong, God is ever pardoning, all-powerful." Pardon sits there alongside good done in secret, which is where most of it happens anyway: quietly, with nobody watching, and no acknowledgement coming back.
The Qur'an is direct about people who never come around. Believers are told to forgive those "who do not look forward to the days of God", and the reason it gives is that God "may repay a people for what they have earned." Your side of the account closes and God's stays open. Forgiving in that sense asks nothing at all of the person who wronged you, and it leaves your account of what happened intact.
The words used for it describe a manner of conduct. The instruction to "forgive with a gracious forgiveness" arrives in a passage about the hour coming, so the graciousness is measured against how long any of this lasts. Elsewhere it is to "pardon and overlook until God brings his command", which puts a term on the waiting without saying how long it runs. Both leave your feelings out of it, which is a mercy when the feelings have not moved yet.
Naming what happened stays open to you. The rule against airing evil speech carries an exception for "one who has been wronged", and those "who defend themselves after being wronged" are told there is no blame against them. Room is kept for the account to be told and for redress to be sought. What forgiveness releases is your claim on the outcome, and you can release it while keeping your distance.
Whatever goes unpaid is still recorded. The scales set up for the day of resurrection bring out even "the weight of a mustard seed", and no soul is wronged in the least. That is the ground under the instruction to turn away and say "Peace." The case is already held somewhere steadier than your memory of it. The Qur'an leaves a door ajar too, since God may yet "bring about affection between you and those of them you now hold as enemies", offered as a possibility with nothing demanded of you now.
Whether to reconcile, to keep your distance, or to say any of this out loud depends on things about your life that a page cannot know. If what comes before forgiving is where you actually are, verses about betrayal and verses about anger sit closer to that.