I don't like global vars (even in disguise). So thats my take on yours.

#!/usr/bin/perl
use strict;
use warnings;

my $amount = 16;
my $coinset = [5,2];


sub change {
    my ($cset, $amt) = @_;
    if ($amt == 0)    { return [] }
    if (@$cset == 0)  { return "" }
    my $coin = shift @$cset;
    if ($coin > $amt) {
      print "$coin > $amt\n";
      $coin=change($cset, $amt);
      return$coin if!ref$coin;
      return[$coin];
    }
    else {
      print "Checking $amt - $coin\n";
      my $rval =change( [$coin, @$cset], $amt - $coin );
      return[$coin, @{$rval}]if ref $rval;
      print "Exception forces backing up to $amt\n";
      return [@{change($cset, $amt)}];
    }
}
use Data::Dumper;
print Dumper(change($coinset, $amount)), "\n";
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