Variable $_ is a global variable and loops like while does not preserve original value of $_. If you use foreach loop inside while loop, that will be fine, since foreach loop preserves original value of $_, whenever loop ends, but while doesn't. So, you should use another variable, for simplicity, and continue ...

     #! /usr/bin/perl -w
     
     my @test_array=(

         'Element2',
         'Element3',
         'Element4',
         'Element5',
         );

     my $item;

     foreach $item (@test_array) {

         print "\"$item\"\n";
         &do_something();                                     
         }

     print "\n";

     foreach $item (@test_array) {
         print "\"$item\"\n";
         }

     sub do_something
     {
         open(IN, "$0") || die("No file");

         while (<IN>) {
             # Do nothing, in the real software we would do something
             # with the content.
             }

         close(IN);
     }
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