Dear Ksumi,
Any employee id of ex employees should ideally be not given to any new employees. Almost all corporates do not allocate the employee ids of their left employees to their new employees.
The major issues which can arise if you allocate the old employee ids to a new employee is, that when working on employee data of for any reference, you or the software you are using (if applicable) will not be able to get proper and accurate information about the employee. There is a possibility of clashes of employee ids.
Incase, if you are using a software, then the software itself will not allow you to allocate the old employee id to a new employee.
Therefore, I suggest that you allocate a new employee id to every new employee categorizing it and in serial order.
Hope I have cleared your doubt.