But isn't the meaning of "if and only if" kind of a condition to be fulfilled? How can a counterfactual condition in the past ever be fulfilled? It didn't happen. I quite agree with Glenfarclas that the only way I can interpret the situation is that of regret, which is conveyed through "if only".
Tom could have started work again only if he had apologized to the manager.
(= Tom could have started work again, but only providing that he had apologised to the manager.) Tom could have started work again if he had apologized to the manager.
(= Tom did not start work again because he didn't apologize to the manager.) The difference between this version and the previous is that one could argue that there might have been other circumstances under which he might have resumed work. He could have started work again if his father had gone to the manager and guaranteed that his son would not give the firm any more trouble.