How can I mend the damage I caused to someone in a car accident when I couldn't find them after we agreed that each of us would fix his own car?

As long as the man has voluntarily relinquished his right to compensation for what befell him, there is no blame upon you. However, if you strongly suspect that he abandoned the lawsuit out of shyness, and you were the one who wronged him and could not reach him, then give charity on his behalf equivalent to the value of the damage inflicted upon his car. If one despairs of knowing the rightful claimants, then he should give it as charity on their behalf.