What if a person has no intention to hurt anyone and then by mistake hurts others. An example is someone who is intoxicated, drives home (with no other way to get home), and then in the process of driving, hits another car and injures the driver of that other car. If this action was not deliberately unjust (chosen as something unfair), can I still forgive?
Even unintended actions can be unjust. Let us take your example of the drunk driver causing injury or death. Although the accident was unintended, it is still unjust because the person knew that he or she would be driving. Starting to drink that evening was not wise. Surely, before the person became drunk, he or she had the rational faculties to know that the amount of alcohol consumption was not good. So, prior bad judgements before the accident show that the unintended consequences had bad choices connected with it. Those choices were unjust choices and so those injured or those who lost loved ones can forgive if they so choose.