Assuming you want a failure if an element from array1 occurs twice in array2, and array1 and array2 don't contain references, I'd do:

my @array1 = ...;
my @array2 = ...;
my %hash = map {$_ => 1} @array1;
foreach my $e (@array2) {
    next unless exists $hash{$e};
    die "Failure" if --$hash{$e} < 0;
}
die "Failure" if grep $_, values %hash;
print "Success";
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If it's ok an element from array1 may occur more than once in array2, I'd write:

my @array1 = ...;
my @array2 = ...;
my %hash;
@hash{@array1} = ();
delete @hash{@array2};
die "Failure" if %hash;
print "Success";
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