In Freshservice, closed tickets can be reopened when a requester replies by the default ticket workflow automator, Reopen tickets when requester responds. You can turn off this automator to prevent closed tickets from reopening when a requester replies. 
It's important to note that disabling this automator will affect all closed tickets, not just individual tickets. So if you want to keep the option to automatically reopen tickets when a requester replies for some tickets but not others, you'll need to use a custom workflow automator instead.
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