Here having ‘the’ changes the meaning completely. The second phrase ‘in case of…’ is used to refer to an emergency or some unexpected plan. For example,

‘In case of fire, exit from this door’.

and

‘I’ll take an umbrella in case it rains’.

On the other hand, ‘in the case of’ is usually used to refer to a situation that the writer has already mentioned. For example,

‘In the case of a customer complaining, we would take action immediately’.

Another example is in reference to a legal case.

‘In the case of Kramer v. Jones, the judge ruled in favor of Jones’.

A common mistake that I see is people using ‘in case of…’ when they mean ‘in the case of’. Once again, ‘in case of’ refers to an unexpected or undesired situation, like rain or an earthquake, and ‘in the case of’ is used to refer back to a previously mentioned situation.