Here ‘case’ has the meaning of situation, the position in which one finds oneself; and this position in the circumstances surrounding it. If the circumstances change, the situation (i.e. the case) changes also.
We can for instance, take the case of Mr Gregson, a well-to-do bachelor with a large house, who agreed with his friend Mr Eddy that this second gentleman should occupy the whole of the top floor rent free. Then Mr Gregson lost most of his fortune in a disastrous business venture and was forced to tell Mr Eddy that he had no alternative but to charge him three pounds a week for the rooms he occupied. When Mr Eddy reminded him of their original agreement, Mr Gregson claimed that circumstances alter cases – that the situation had changed.