Is it possible to disable an instance or a connector in Community edition?
OK, but I still am not 100% sure what you mean. You want a process to stop sending emails, right? So, take away the circumstances which either cause it or allow it send the emails.
You can either:
* Remove the email connector from the task
* Remove the task from the process
* Change the condition that causes the task to occur
All of these will work.
I'm new to Bonita, but as far as I know, a 'case' is the outcome or evidence of a process that is yet to run or already has run:
A case isn't something that can be 'enabled' or 'disabled', it just exists.