I translated your map{} into the equivalent foreach() statement.
All map statements have an equivalent for() or foreach() loop.

use strict;
use warnings;
use Data::Dumper; 

my $this_key = "NOT_IN_HASH";
my $hash_ref = {};

my @items;

@items = map { $_->{value} } @{$hash_ref->{$this_key}};

print Dumper \@items;

my @x;
foreach (@{$hash_ref->{$this_key}})  # loop does not execute
                                     # because array is empty
{
   print "loop is looping\n";  #This doesn't ever print !
   push @x, $_->{value};
}

print Dumper \@x;

my @nothing;
print Dumper \@nothing;

__END__
Prints:
$VAR1 = [];  #print Dumper \@items;
$VAR1 = [];  #print Dumper \@x;
$VAR1 = [];  #print Dumper \@nothing;
[download]