‘In the case of’ is used to refer to a particular object or situation as in: In the case of people arriving late at the theatre, the manager has the right to stop them entering the auditorium. In other words ‘in the case of’ here suggests - when/if that happens.
‘In case’ suggests ‘if’ together with a sense of precaution or early warning as in: I always take an umbrella with me in April in case it rains.
I like the idea of the contrast between what you wrote and I wrote but I’m not really sure yours works. I think the following sentence after the ‘in case’ sentence has to be a positive action. The idea would be: 'In case people arrive late, the manager leaves a side door open.