Your code will never assign a value to $2.
If I understand correctly you want to change to $ to a literal "dollar" if the string after it is not a key of the hash.? 
$line =~ s/(\$)(\w+)?/$2 ne ""?(exists $words{$2} ? "$1$2" : "dollar$2
+"):"dollar"/eg;

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In reply to Re: Use of uninitialized value in concatenation by Utilitarian
in thread Use of uninitialized value in concatenation by gem555

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