Minor nit:

unlink "$file_name";    # you don't need the quotes here
unlink $file_name;      # ... so suggest you write it like this
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More importantly, you are currently ignoring all unlink failures. Are you happy to ignore them? What are your error handling requirements?

If you simply want to write a new function, please don't call it unlink.

OTOH, if you really, truly want to override the built-in unlink function, that is an XY Problem and you need to tell us the real underlying problem you are trying to solve, why you think overriding unlink is a good way to solve it, and what alternatives you have considered.